If you speak to an old-fashioned clock repairer they have ultrasonic baths they use with special solvent to vibrate the microscopic crap out of tiny watch parts. He/She may do it for a nominal charge, or advise you of the solvent used - in the 70's when I was associated with instrument makers it was a highly volatile hydro-carbon something like acetone. It will remove every element of human or other gunk, but probably needs the ultrasonic agitation to get deep down clean. There is minimal heat involved.

Otherwise search the Yellow Pages for watch-makers supplies - they could give some free advice.

Regards
John