It would most likely be integrated into Canada at the same time British Columbia or maybe even the Northwestern Territory are added to Canada, simply because that early Alaska generally was just a money drain (Alaskan fur trade was essentially dead, which is why Russia sold it in the first place, gold wasn't yet discovered) and Britain wouldn't gain ANYTHING if it were to keep it (unlike the case with Newfoundland, which at least had VERY lucrative cod banks). And well, I basically see Alaska as another Northwestern Territory, if not directly integrated into it (at least up until the point where the Yukon Territory was created, which which it would then be lumped together). It would be fascinating what will happen with the Alaska panhandle. In case of it being lumped together with NWT I would see the panhandle going to BC. Also "rump Alaska-Yukon" might even get province status later (ca. 1930s), considering how population grew in Alaska in OTL.