I have a 1980's vintage SR Semi-pro with a Shimano 600 EX rear derailleur. That derailleur comes in two versions: short cage and long cage. The one now on my bike has a long cage. My largest cog in the rear is 27 teeth.

The pins/rivets that hold the parallelogram of my current rear derailleur are somehow loose, due to a crash, or just wear and tear, so that the parallelogram is no longer a true parallelogram, but rather is deformed. This causes the derailleur cage to be bent relative to the chain-line.

I scored a similar derailleur off eBay with the short cage; the pins/rivets on it are tight. Can I swap the cages? If so, how hard is that to do?

Thanks in advance.