@SuperDuke If you're not going to bother with an apostrophe on what is obviously a possessive, you may not wish to call attention to the omission by adding the 's'. The shorter form indicates that the apostrophe and final 's' may also be considered things you don't give a fuck about.
Also, the added 's' is unnecessary. Unnecessary letters, like unnecessary words, should be omitted.
For a truly professional tone I'd suggest using more syllables, e.g. "On the behalf of every imaginable fuck...."