Is there any where inside the game where the damage stats for weapons can be determined? I know that information is available outside the game on various websites and was also published in the hint book back in the day, but that seems like cheating. How, aside from cost in the store, do you know whether one weapon is necessarily better -- or how much better -- than another?

You don't really. That was pretty common for the time period.

No in-game way.
You need to write down all the damage done with each weapon, adjusting for the wielder's strength, if you don't want to "cheat". Eventually you will have enough data to be pretty sure of which weapons are best, but by then the game is probably over.

The hint book is included in the extras from GOG, and it's a searchable PDF, so you can minimize spoilers by searching for the weapon in question. That's what I ended up doing. Otherwise, selling prices can give you a sense of what's best, but that's really tedious to check. As others said, there's no clear way to learn these stats in-game.