When I did this, I put a 1/4" dia steel rod (may have been a mold pin, or piece of drill rod I had) in the vice, and then a rag over top of that.
Then I carefully used a small ball peen hammer to peen the rivet over - you know the old school method.
The rag kept from scuffing the rivet and the clock face. I did it by myself, but a second pair of hands might have made it easier. Just had to make sure the rivet was on the pin before each tap.
In the end, there was some minor burnishing of the paint on the rivet head. I'll try to take a photo if I can. But to me, it's not that noticeable.