I was wondering how you'd work changing the Tydirium to a freighter when it's named as a shuttle twice in dialogue, but I realised that'd be a relatively easy cut:

Madine: We have stolen a small Imperial [snip] cargo ship. [snip] Using a secret Imperial code, a strike team will land on the moon and deactivate the shield generator.

I suspect cutting Piett's reference might be a little harder. He says it very fast, and if you just cut the word "shuttle", it's less clear what Tydirium refers to, given it's the only instance of the name in the film.