If I understand what you want to do, an easy way to do this would be to make a small router compass. The smallest one I use for inside cuts is a piece of 1x6 poplar with a 1" hole for a template guide. Then mark off your radius on the compass and drill a tight hole for your nail. On small inside cuts, where the piece is going to be pretty much covered up by the router the whole time, I like to double stick tape the parts to my cutting board, so that the center piece won't bounce around when cut free.
I like using the thick boards for compasses because they don't flex, they don't wobble on the pivot hole after a couple of uses, and because some of my template guides are kinda long.
The only other way I could think of doing it would be to use your existing plate as a template, but unless you had a spare plate that can use guide bushings, that might be more work than necessary.
For making small outside cuts, I have a base plate for my router table that I have drilled as a compass, and it works pretty well for small circles if you rough cut the circle out on the bandsaw first. (good for plaques, toy parts, etc.)
Hope these ideas help,