In my region 'kasse' is never used to mean 'box', so it wouldn't be ambiguous, but I can't say for other regions. We still have 'postkasse'(mailbox) and 'verktøykasse' (toolbox), but 'kasse' alone would always mean 'cash register'.
Is there a way to distinguish the two senses of the word besides context? I.e. if there is any chance of confusion, one can say "cash register" in English to make clear that one isn't talking about some other sort of register.