While going to extremes with hammers to secure a seed phrase: I've seen good things about titanium hammers (on Youtube, I never tried it). It's supposed to be
lighter, vibrates less, and transfers more of it's energy. But I assume you're not going to do this for 8 hours per day, so it really doesn't matter much.
I took the opportunity to look into this video. Let's put the vibration thing aside, because it's more important for people who work a lot with such tools on a daily base. If someone doesn't know what to do with his surplus of money, maybe get a titanium hammer. You could buy a bigger hammer head so you won't miss the letter stamp while still being lighter than a steel hammer. (Ear plugs will be the way cheaper solution if you mind the impact noise.)
By my own experience with stamping washers: the more mass (inertia!) you have where you put the washer on the better it is, ideally an anvil or something similar sufficiently heavy and suitable from the scrap yard. You can even put the anvil on something that isn't too soft but provides some dampening. It's physics, laws of nature, transfer of momentum, the ratio of mass of your hammer and the anvil.
I wouldn't use a wood, rubber or stone hammer to hit a metal stamping tool to imprint metal washers. Use a steel hammer that can transfer enough punch comfortably and allows you to hit the stamping tool with confidence. Have a rigid support surface of way more mass than your hammer where you put the washers on (be it an anvil or some heavy (cubish) block of metal from the scrap yard).