I don't think there are any rules on which country the captain is from. Personally, I think they'll stick with a British Davis Cup team for the time being at least. Let's face it, Britain struggles as it is, never mind splitting the talent.
Scottish tennis won't want to miss out on all of that lovely Wimbledon money, and the rest of the UK won't want to miss out on their best player in generations.
If Ireland can stick with a joint rugby team, it shouldn't be that hard for Britain to stick with a joint tennis team.
Good point Sparkle! Also I agree with the rest of your post, and certainly as far as cricket goes, not that I'm a follower, but some Scots do play at English county level as well as for the national team, and in fact one Scot, Mike Denness, was once its captain. The curiosity here as that some of these players also play for the fledgling Scottish national team as well as representing Scotland in other sports.