[Lost in the 60's]

Check prices on a replacement and you may well be looking for a reputable repair shop, if any still exist in your local. Repair shops have all but disappeared around me. I can't find a copper/brass rad for my '89 C3500, they have all gone to aluminum.
Soldering that nipple back on is no big deal for a shop. They will, most likely, remove the tanks to rod out the tubes, or suggest replacing the whole core.