I've used errors before as a negative hitting stat. Decided to get rid of it after that year.
I have also used double-play, but it is the worst stat I have ever experimented with. Clearly, first basemen are going to get a point for every double-play turned.
Outside of those two my experience is limited. I'd probably stay away from fielding stats, if for no other reason any DH on a roster is going to have obvious advantages/disadvantages.
People ask me what I do in winter when there's no baseball. I'll tell you what I do. I stare out the window and wait for spring. ~Rogers Hornsby