On Sunday, April 14, 2019 at 7:43:32 AM UTC-7, Expiring wrote:
I have a few almost new usage-wise, but very old, tools with rubber
handles. I want to keep using them.

The rubber surface has become gooey and sticky and comes off on my hands.

Yeah, flexible polymers age poorly sometimes. If you can remove the rubber
entirely, and clean the handles, there's rubber fusion tape (made for
electrical splicing, but more widely useful) that can be stretched/wound around
the handles and it cures to a good rubbery grip.

If you want it to last forever, instead of just a decade, it's available
in silicone, too, though that might be more slippery

https://www.3m.com/3M/en_US/company-us/all-3m-products/~/3M-Wrap-Repair-Silicone-Tape/