An Android HTC phone would be used with it in case you forget your phone and lock your keys in the car and can't remember anyone's number. It tends to be harder to forget a watch.
In practice, that means you'll be looking at Android Wear, Gear S2 or a Pebble Time model (original/Steel/Round). I don't believe Android Wear stores contact info locally, although you could theoretically create notes. As for the others, I can't honestly answer at the moment -- even doing some research doesn't turn up much.
I'd go into it assuming the answer is "no." But then again, the odds of needing a phone number you don't remember and forgetting your phone (but not your watch) aren't very high. Heck, if you have the right watch, you can make a phone call from the watch as long as you're close enough to the phone in the first place.