In my opinion it would seem a little silly as a guest to not ring housekeeping calling to their attention that the remote is stickey and should be seen to straigt away by either attempting to either clean and/or replace it. Drawing attention to the fact that I as a guest think nothing of the condition of a filthy, sticky remote and accept its filthyness by cosmetically covering it further with a Ziploc, exhibits my acceptance and tolerance to stay in a room that has not been made up properly to the extent that such room should be out of order. I would demand that attention by the hotel to either assign me another room or correct the problem and not stay in filth.
Like going into the coffee shop and noticing a stained cup on my table... I surely wouldn't attempt to put the cup in a Ziploc.