The first thing is, you don't want to completely drill the rivet out. If you try to drill the rivet out completely and you're off center a little bit you end up with a oval shaped hole. You just want to drill or cut the rivet enough so you remove the head on one side. You can use a drill or angle grinder for this.
If you drill:
1. Use a sharp center punch to dimple the center of the rivet head so your drill bit won't slide around.
2. Use a 3/16" bit and start drilling the rivet head slowly, when it looks like you're getting close to being drilled through the rivet head stop drilling and use a sharp cold chisel and a hammer to check the rivet head for looseness by gently trying to cut the head of the rivet with the chisel. If the head doesn't lift off drill a little more and check again.
3. When you get the head of the rivet removed use the center punch to drive the remainder of the rivet out of the hole and presto! You'll have 2 nice round factory holes (one in the brace and the other in the hull) that line up perfectly.
Go slow on your first 2 or 3 holes until you get the feel for removing the heads and then you can speed up.
You can also use a grinding wheel in an angle grinder to cut the head off of the rivet instead and punch the body of the rivet out with the center punch, but again... be careful and go slow until you get the feel for it.
To reinstall your brace, use a couple of 3/16" machine screws and nuts to line the brace up with the holes and hold it. Dip your rivets in some marine epoxy or 3M 5200 and install them in the holes with the setting tool. Remove the 2 nuts and screws and install rivets.
What kind of wood do you plan to use and what kind of glue to bond it together. What do you plan to seal your wood with?