Cleaning Around Handles on Oak Veneer Cabinets?

I've read the many questions and responses. My question is a little different. I have 1960s light stained oak veneer cupboards in my kitchen, all original. I have kept them clean, but there are some cupboards that have stains around the handles from many years of cooking hands prior to us. I don't want to take the finish off. Is there any recipe that would remove this safely? Or do I need to think about refinishing all my kitchen cupboard doors? I'd like to avoid that if possible.

By Cynthia F