If you have to open with that, all others in the enclosed room with no windows or ventilation now realize they are in trouble. You obviously have inside information that the recipients in the room are not aware of. Either you are not 100% sure if your feet stink but think there is a high possibility or you KNOW your feet stink yet you are going to take your shoes off anyway.
Regardless it leaves the rest of the folks unable to do a thing. They do not want to pardon you if your feet stink in fact they probably would appreciate it if you did not remove your shoes. "Pardon me if my feet stink" does not allow for any option and you should just say "Listen, my feet stink and that is just the deal and I am taking my shoes off anyway."
One can ponder occasions when a pardon could be given for stinky feet but not many come to mind. In fact I can only think of one: At the beach, with the exfoliating sand and surf, salt air and lots of wide open space. So, if you have to open with "Pardon me if my feet stink" before removing your shoes and you are not at the beach with lots of wide open space the shoes stay on.