you and the people you are meeting decide who will book the room. then you agree on who pays what to whom. there is no cheating anyone.
there is no sneaking about, you just go about using the rooms as a sensible guest. any kind of silly behaviour or talk will simply make you feel and look extremely foolish.
otherwise the enjoyment is yours.
People staying in hotels invite guests in for all sorts of reasons: visiting friends or relatives, holding business meetings, all sorts of purposes other than for sex. Just walk in as though it's perfectly normal. I agree with others about sorting out with the couple who is paying for the room, that's an entirely separate matter.
first thing to decide is:
Will someone be staying in the room after the fun has ended, ie till morning ?
Will the other people involved be going home or will they need a room to go back to after the fun ?
Have you all met before ? if not we would book a room ourselves and let the others book a room(s) then decide which room to play in on the night, at least then if things didn't pan out the way we hoped we would have somewhere to retreat to and somewhere to spend the night.