try moving the top hair one way, bottom hair other without redrilling.

As long as the handle will cover.

Worst case scenario if the handle won't cover, you can add backplates.

Are the cabinets painted, so you could sand the wood putty and touch them up? If they are stained, the wood putty will most likely always show some.

Just make sure the putty you choose gets rock hard, not the soft type of wood putty.