I am no expert but I just want to share my findings from my hand pumps.
After looking inside my hand pumps, i found almost no metal to metal contacts. In fact too many orings to keep up.
If one can't find a trusty silicone grease, just get a small tube of hill grease (a bit pricey) and save yourself a headache. It should last a while and use a VERY thin coat on shaft when needed.
I like grease better than oil because oil does not stick like NLGI2 type silicone grease. Hill grease, molykote , diver grease and etc.
And Non petroleum +1
Also a decent moisture filter would help.
Hope this helped