If you have to write this many times in a piece of text, and there is no possibility of confusion of $s$ being an actual set of elements you are removing, it is okay to first write one sentence reminding the reader of this abuse of notation ("In the following, we write $S\setminus s$ to mean $S \setminus \\{s\\}$") and then write $S \setminus s$ thereafter. But otherwise I would recommend using the proper notation.