Just to locate these options a little better, Carvers Gap is around NOBO mile 374 from which you're talking about going north about 14 miles, and Watauga Lake is around mile 424 (these are both relative to Springer Mountain), and your second option is to walk south to that from where rte 91 crosses the AT at around NOBO mile 442.

Going north from Carver's Gap has some ups and downs, and can be windy on the balds there --- though I hiked that in late March last year when it was pretty cold out still. The Overmountain shelter is moderately cool as a converted barn (was quite "cool" when I was there --- lots of large gaps in the walls of that barn).

From my recollection, I think you'll find the shorter distance more hilly/climbing, but perhaps a bit more scenic with the balds in there, whereas the Watauga lake stretch you're considering might be a bit better/easier trail overall.
In general I wouldn't think that water or shelters would be a problem.

Caveat: I've only been through there the once; pay more attention to anyone who has a more frequent/intimate knowledge of that area.
_________________________
Brian Lewis
http://postholer.com/brianle