I just checked how my Apple Watch behaves for tracking, and it seems to appear independently from my iPhone and iPad when I look in the Find my iPhone app. However this requires to have the watch and the iPhone on the same Apple ID account, which would mean all your messages got shared to the watch on another person’s wrist. For someone with Alzheimer’s that could be very confusing so I think Find my iPhone is not the best solution.
I looked at the Find Friends tracking app which would allow you to have the watch linked to your husband’s iPhone, but this doesn’t appear to discriminate different devices so easily. I have a friend with at least 3 devices, and I have no idea which one is tagged in Find Friends.
In summary I think Apple Watch alone is not the ideal tracking tool for monitoring someone with Alzheimer’s. It would probably work but with some limitations and it is too easily disabled by a confused person. If I had your problem I would be looking for the local Alzheimer’s support groups to see what other careers had found most effective, and also asking local Social Services and medical support professionals what they have found to be most effective.