Call the front desk and ask them to 1) hold all calls; and 2) what is the latest "late" check-out you can have. Let them know you will be coming down to check-out at the time they give you to be out of the room.
It doesn't matter that you will not be receiving calls. This request just sets the stage for the late check-out. They won't question your request for late check-out, or call your room to "check" to see if you have left. Gives you a bit longer with regard to privacy and provides "plausible deniability" in the staff's mind -- no reason to enter the room, you have asked and received a late check-out, so they will not enter the room until you do not come to the front desk to check out like you said you would.
Hang your "do not disturb" sign on the door of the room.
Do "the deed" either in the bathroom, or in an adjacent place in the room where you can hang a sign on the door that says "Do not enter. Dead body inside. Call police."
In my opinion, that is the best you can do with regard to at least limiting any trauma an innocent hotel employee may encounter.