I have (have had) really sensitive skin, and it took me a few years of trying a variety of cleaners to get to where I can touch white bread/cheese/women w/o leaving grease prints.
I use 2 methods,
#1 is to work smarter and minimize getting really nasty in the 1st place.
no need to be girly and avoid work. just be smart about it all.
#2 is old school BORAXO powdered hand cleaner, like the kind they used to have in shops and restrooms. it's still available thru janitorial supply or I buy in 5# box from Amazon.com.