It is not unusual to want to replace old hardward when you are refinishing furniture. The problem is that the holes will most likely not line up. So filling the holes is the best option.
With this project I filled the holes from the original drawer pulls on this dresser. I am flipping this piece and wanted to replace the old hardware with single wooden knobs.
I use Dixie Belle Mud to fill the holes. That usually wil take a couple of coats, little sanding, and once you have completed your painting it will be ready for your new hardware.
Directions how to here: