Well here's a creative hack - you could install a second 64-bit perl and have it wrap COM objects with a quick and dirty REST web service, then replace the COM calls in the 32-bit perl with web requests to the web service!

Of course if the whole program is all about COM calls, that isn't very practical, but if you only need COM for a few edge features, like exporting to MS Word, this could be faster than fully debugging the app on a new perl environment with new module versions.

Am I guessing correctly that you don't have a copy of the perl environment that this app runs in? Because otherwise you could locally build a whole new 64-bit windows perl environment with all the same module versions, and bring that to them on a thumb drive to quickly replace the existing perl environment in a short visit.

If you don't have a copy of that perl environment, you should probably ask if you can make one. It's in the customer's best interest if the versions are known and recorded somewhere.