Stating the obvious, "the problem" is not which tasks you may or may not do as a corporate pilot while keeping your dignity (and the bar is sometimes pretty damn low in our world..), but much more the relationship with your chief pilot, or whoever asked you to come in and do this job.
Operating an expensive jet, I don't see how employing cleaning personnel is going to break a flight department's budget... So is this not much more about somebody place above you in the pecking order thinking that you have it too cushy and wanting to make a point? If so, it's a leadership problem, and a good discussion about mutual expectations is what you are looking for.
My opinion: if I like my job, my boss, and my chief pilot, I'll come in on a slow day to do pretty much anything, and that includes (actual examples) getting condoms and sex-toys for the boss' dirty week-end, take the flight department's office staff through the airplane for a familiarization brief, scouring the shops for a portable milk-foamer for our galley, sourcing child-friendly sleeping masks, ... the list goes on and on.
Basic condition for me giving "a little extra effort": feeling appreciated and being taken seriously as an employee. If those conditions are not met, you got way bigger problems than spending a day glossing the leading edges....