Now I'm not saying it couldn't end up that way but most people seem to think an internal pan handle dispute would go BC's way, if that's the case I don't see the territory being added to AlaskaWhat @metalinvader665 says bears repeating. In OTL the Stikeen Territory was merged with British Columbia in 1863, there's a good chance that in a TL where Britain gains Alaska from the Crimea this might be attached to Alaska because it's closer.
https://en.m.wikipedia.org/wiki/Stickeen_Territories