"Waiter, we'd like to order."
Why not 想 in this case? Isn't 想 usually used for "would like to <verb>"?
I think 想 should be accepted, especially since when it gives the sentence "I'd like to order" the accepted translation is 我想点菜 while 我要点菜 is not accepted.
想 and 要 have very similar meanings and it doesn't necessarily imply the same notion of politeness as in English! 要 makes sense here because it's a decision that's already been made and you're taking action on it, while the direct translation may seem too rude in English! So I think that, considering the actual situation, "would like to..." seems to be a good translation!