Is it possible to swap out the cups and lock ring of a Hatta Swan BB for cups and lock ring of another brand as long as they are the the same type - 68, 1.37x24 and reuse the original spindle for a square tapered bb? The cups are trashed on a vintage bike I have, but the spindle is still fine. I was thinking of just buying replacement cups, ring, and bearings.

Sure, as long as the cups are reasonably close in thickness and designed to use the same size balls (the vast majority of bottom brackets use 1/4" balls but there are a few exceptions). If the replacement cups are markedly different from the originals, you may chainring clearance issues or be unable install a lockring.