I had this issue with an old dresser I refinished. I ended up finding pulls that covered the existing holes, so I had to drill new holes for the new screws. You can see in the pic how the flat pieces on the ends cover the old holes. I never see the inside of the drawers, so no big deal. A cabinet door may be different since you would see the old holes. You could maybe fill them with something.

There are still some pulls out there that have a shank but they are few and far between. I just can't recall the company names.

Thanks for your suggestions, I think I will try spray painting the existing pulls and see how that goes.