ask your dentist, and the hospital dentist. it certainly used to be the case that dentures were fitted immediately, or almost immediately, so that as the gums heal, they heal to accommodate the dentures and get a good fit. things may be different these days though.
as to how you broach the subject, it's your teeth and your smile and very important for your self-esteem and confidence, so just ask. i'm very surprised no-one has discussed this with you already. ask, ask and ask again, until you're completely happy and understand the whys and wherefores.
good luck with the dentistry and heart surgery.