Well, two things, firstly that NATO membership and an anti nuclear stance is not incompatible - Denmark has a pretty much this situation at present with a firm commitment to no nuclear arms on Danish soil but remains as a NATO member.
There are a number of other NATO members with stated objections to nuclear weapons as well so that's not a biggy.
My understand is that is that the anti-nuclear positions of some current NATO member-states was in effect prior to the formation of and their respective entries into NATO.
Since then, there have been changes made to the conditions of NATO membership for new member-states, to prevent the nuclear policies and positions of those new NATO members from hamstringing the deployment and operations of nuclear armed/powered forces of other NATO members (i.e. the US, UK and to some degree France). Not sure if these changes are something as formal as written conditions of membership in NATO for new member-states, of if this is more a policy of the US and/or the UK vetoing the new membership requests for anti-nuclear nations.
With the above in mind, I would not automatically assume than an independent Scotland would be allowed into NATO. This is partially due to operations and deployment issues which USN subs and carriers would have, but also due to a requirement to defend Scotland in an emergency which could be a burden for NATO members. Given what seems to be low numbers in terms of personnel and force assets, what appears to be the current proposed force structure would require outside assistance if there was any high intensity activity in Europe which threatened an independent Scotland. IMO the numbers as currently given are questionable in being able to maintain the required level of patrolling and enforcement of what Scotland's likely EEZ claims, SAR and constabulary responses would require.
In terms of force structure, if a future Scotland wanted to have assets available to respond to something at a given moment, then in reality Scotland would need 3x the desired # of responding units or more of that particular asset in order to provide that response.
Assuming the Royal Scottish Navy was reconstituted with a pair of Type 23 frigates, that is an insufficient number of frigates to guarantee that one is always available for operations. Even more so if one of them is sent out on a deployment or engaging in Show the Flag visits. Now add in some sort of amphibious/sealift vessel, and at best, both vessels might (emphasis on MIGHT) be available to deploy as escorts, but those would be insufficient IMO to provide a safe escort in moderate to high threat environments. Deploying both of them (if they could even be surge deployed at the same time...) would also then leave Scotland without any warships in home waters available for anything should there be a threat to Scotland's SLOC.
Scotland would need three frigates to provide one available, and four would be better. Especially if Scotland were to engage in contributing to international actions or deployments like anti-piracy patrols off Somalia or Nigeria, overseas HADR, etc. More frigates, and/or more capable frigates would be required if Scotland wanted to be capable of deploying an independent task force in any area of greater than a low threat level.
On the air side of things, a dozen Typhoon fighters would be sufficient to have two flights available for domestic air intercept duties. In the event of an overseas deployment or high tempo operations, there would be at least gaps in air intercept coverage of Scotland, if not gaping holes. Similarly a half-dozen Hercules air lifters would leave a pair available for operations at any given time. Depending on their condition, level of use and maintenance schedule, it could even be less than that. Something which the Kiwis found during the crisis in Thailand, when none of the five RNZAF C-130H Hercules were available for deployment. If memory serves, one was in the process of being deployed but had to return to NZ due to an equipment failure.
For the land force, three infantry/marine units might just be enough to support one being in the field for a long deployment. This is assuming that the capabilities of the three units are all essentially identical and that any support functions which the unit in the field requires can be met without overtaxing the support capabilities of the land force. Given that only two light artillery, comms and recce units are mentioned, and a single unit each of engineers, transport, logistics, and medical, unless these various units are capable of sub-unit deployment while meeting the required deployed service tasks, then there is insufficient supporting units to sustain a deployment. At least not without drawing the needed support from another nation.
Also of note is that from the plans I have seen, there has been little mention of any sort of training establishment so that new personnel could be brought into a Scottish Defence Force. Resources would need to be allocated to setup any such training establishments which Scotland would not already have, but also to sustain any existing or newly created facilities. Further, personnel would need to be assigned as instructors and then students, along with training kit appropriate to whatever was required for the skills and roles to be taught.
These, and the above mentioned unit and asset numbers are where larger defence forces and militaries can encounter economies of scale. The RN for instance only has three OPV's in UK home waters for patrolling, which means that only one or two is likely out patrolling at any given moment. However, there are also 19 RN destroyers and frigates, of which a number of them can be tasked for patrol around the UK if needed.
Something which I have not seen addressed, what would happen with current 'Scottish' RN, Army, and RAF personnel. Presumably some of them would wish to transfer from their current service into whatever the Scottish equivalent was. What would happen if there was either no appropriate, or insufficient numbers of appropriate roles for those wishing to transfer in? How about if there no, or insufficient numbers of slots at various ranks? Going further with that, what happens to 'Scottish' personnel serving in the RN, Army or RAF who do not wish to transfer to a Scottish Defence Force? I could easily see how a Major in RTR not being keen on transferring from the British Army to a hypothetical Scottish Army, since the type of British unit the Major would have commanded would not exist in the Scottish Army as currently outlined by the suggested plans.
Lastly, if Scotland were to keep the defence budget at roughly the current rate of 2.5% GDP, I get an annual defence budget of roughly £3.4 bil. or about 9% of what the current British Armed Forces defence budget is. What level of personnel, operations, equipment and more importantly capability would that realistically sustain? How well would that really fit with how a Scottish gov't would see a Scottish Defence Force, especially the first gov't which would likely leave a lasting impact on the future shape of any Scottish Defence Force? How would the Scottish Defence Force, particularly the capabilities and operations, especially those overseas, fit with what or how the people of Scotland would see 'their' defence force? This last bit is in mind because as part of the UK, the people would be used to the British Armed Forces being extremely capable, and anywhere. With about a tenth the budget, both the capabilities and the reach of Scotland would be significantly less than they were when part of the UK.
These are all things which would need a fair amount of detailed planning to address, which either has not been done, or it has (or is being done) but not announced.
-Cheers