One more vote for Leather Masters. Note that their mild cleaner really *IS* awfully mild...as in, it might not even hurt the dirt
I did a pal's car with Leather Masters after he'd treated its leather for years with various stuff from Zep,
Meguiar's, and Armor All. It was a night/day transformation. The stuff I was cleaning off/out of his leather was just so...YUCK, nasty yellowish [stuff].
If you're using the Woolite, I'd sure figure out a way to rinse it off. Yeah, I know, everybody uses it with no issues, but still....