I have the English SMAS+SMW cartridge and have thought about doing a blind All 5 Any% race with some friends.

However, my question is, since they only have the SMAS version, does switching out the cartridges from SMAS to SMW still count towards the All 5 Any% run, or is it invalid due to the use of multiple cartridges?

I can't say for certain what would be allowed on the leaderboard here, but if it's just a race with some friends, don't let semantics/specifics stop you. Come up with a ruleset and see who's down to play with you.

I think the most logical answer would be that it's not allowed since you would get an advantage over an actual SMAS+SMW cartridge.