~~~I've used about 5 different strops. the last new strop I bought was one of Tony's...I think it is his latest model (Steerhide)...the one on the left-
bought it in October 2011 and I have not used anything on it other than my hand for oil. I'm talking about the natural oil in the palm of your hand. What's important is to wipe the leather before using so as to remove any lint or dust that fell on it since last use...any little bit of detritus will muck up your edge
~~~what I've been doing (right or wrong)...when finished with the shave, I wipe the blade with my damp wash cloth then my dry hand towel. The wash cloth is also used to wipe my face to remove any left over shave soap, but only after I use it to clean the blade...and I dunk the wash cloth in the sink water which is warm, then wipe my face and wring out the wash cloth, then I hang up this wash cloth and dry my hands so I can strop my razor on linen and leather before putting up (and not kept in the bathroom so as to avoid any moisture). After all, that is the idea behind stropping after use is to dry the blade. I make sure my hands are dry before this final stropping so I don't get any moisture on the blade or strop. Strop hangs in a closet around the corner from the 1/2 bath.
Now I go back to the damp wash cloth which is now cool and use it to close my skin pores. Just the coolness of the damp wash cloth on my face is enough to close skin pores. Now it's time to apply after shave, with closed skin pores and I wont get any A/S on my strop or razor. FWIW, I like to apply my A/S after the sklin pores close. Others may have better and different ideas