No, leave the dropouts as is, as long as they are not damaged. Just remove and replace the seat stays in their entirety. If you silver braze to the seat tube you should be OK. Cross Checks have a fairly thick seat tube. If fillet brazing with brass, I would use a heat sink in the seat tube. Using the existing seat stays as "lugs" or "sockets" to slide new stays into could work, but only if they are fairly large and you can find new stays that would fit inside of them.

Dave