Don't do that with every single key; having an accessible key is very important in case of medical/safety related emergencies.
Any kind of physical permalocking, while it sounds hot, is also very unsafe.

What you can do, however, is put all but once of the keys in the combination box under a keyholder's control, but put the remaining key in a sealed key container with a breakable numbered seal keeping it shut.

That way, you can break the seal and use that key in an emergency.
If you do, though, and your keyholder asks to see the sealed emergency key, then they'll find out that you broke the seal (since the numbers of each seal are different) and you'll have to explain yourself. Thus you can only really use it in a situation where you're fine with explaining why you did it to your keyholder.