The idea of a timed safe troubles me a tad as it's possible you might have some sort of emergency. Let's revisit the idea of your sister and mother. If they would agree to hold the keys that would seem ideal as if you asked them for the keys they would presumably know you were going to masturbate and then when done you would have to return the keys. That would be a deterrent, I think. I mean I would not want my Dad to know I was about to masturbate and when I was done.
If they will not hold them, have actual possession, how about putting them in a small container. The container would stay in either your sister's or mother's room but they would not handle them. Would they agree to that? Then they never touch the keys but you would have to enter their rooms to get them which might discourage your access.
Or put the container on the mantle piece in the living room or on top of the TV or up on top of the kitchen cabinets where you would have to get up on a ladder, a rather obvious thing to anyone about.