If, in addition to removing trailing spaces, you don’t mind also removing leading spaces and extra spaces between words, the TRIM function might do what you want. For example, if your column for entries with unwanted spaces is A, and your column for entries with the unwanted spaces removed is B, you’d type =TRIM(A1) in cell B1, and then copy and paste that formula down the rest of the B column as far as necessary.
If you need to preserve leading spaces and extra spaces between words, I think you would in fact have to use regular expressions, whether in a formula or in a search-and-replace. Would something like \h+$ (match any horizontal white space at the end of a line) do the trick? (Sorry I can’t be more helpful here. I use Writer a lot more heavily than Calc, and in Writer I use the AltSearch extension. I end up seeing regular expressions in my search and replace fields but not really having to learn them, since AltSearch supplies them for me.)