The .45 Auto cylinder is 1.53" long, the .45 Colt cylinder is 1.67" long. It would be a one-way conversion, the forcing cone would have to be trimmed for the longer cylinder and B/C gap, which would prevent using the shorter .45 Auto cylinder any more.
Conceivably, you could have the .45Auto cylinder reamed to fit the longer .45 Colt cartridge, and have a revolver like the "short cylinder" M25-3 and M25-4 that were chambered in .45 Colt.
On the M625 info pages of SCSW, it clearly states "not interchangeable", but the series numbers will indicate which cartridge the guns are chambered for. Odd number is .45C, even number is .45 Auto. By the time you got all the work done to convert what you have, you're almost 2/3 the way to the price of a revolver chambered for what you want. Then you'd have one of each.