Put a wheel in the frame, measure from the center of the rim's braking surface to the center of the brake bridge where you would drill the mounting hole- if this measurement is 50mm or a little less just about any dual pivot caliper will work. If it's over 60mm it will fall into the mid-long reach brakes category.
Other than the bridge being too thin, the other problem I see is that modern calipers are made to bolt to a flat surface and your bridge is probably round. The easy way around that is to find some old calipers that come with the concave spacers and as a bonus, they usually have longer reach than newer ones.
All that said, I think the easier and better fix would be to replace the canti studs.