Often you find radios that are very restorable but have handles that need replacing, such as the one in this picture. Removing the old one wouldn't be a problem, and replacement handles can be purchased (AES has some, for example) but it doesn't seem possible to install the new one without drilling out the rivets on the bracket. Is there some neat trick to replacing these handles, while leaving the original hardware intact? It's always a shame to see philips-head screws in place of those rivets, as seems to be common practice.

It seems like you could cut the notch open on the new handle and then sew it back together, but that seems difficult. Anyone got any tricks or tips, or know of replacement handles that are specifically designed to be installed in these situations?

In most cases that style uses split rivets. Sometimes they can be straightened from the underside and reused. More often, the metal is brittle and one leg of the rivet will break off. In that case it can be replaced with a new one. They are still available. I saw some yesterday at my local Tru-Value hardware store while searching for Tinnerman nuts. It takes some artistic finesse to artificially age them to match, but it can be done. The only caveat is that you will damage the wood somewhat around the edge of the hole removing the old rivet, so the new handle will not be as strong. I try not to lift my potables by the handle if they have batteries inside because of this.