Take it slow, wear some safety glasses, (or a face shield/goggles). Don't stress too much about nicking the wheel. As previously mentioned, 80% or more will support the new bearing fine. Worst case, there are ways of dealing with voids and repairing any damage.
+1 80% contact is usually plenty if you do tear it up some. And I usually use a cutoff wheel in my Dremel when cutting bearing races. Another combination would be to cut the races and also use the dry ice. Could make it brittle enough to be able to chisle it out.
Or send it to me, I'll fix it and press in the bearings too (I've got a press. Don't even TRY to get the bearings in straight without one)