How can I install cabinets pulls without drilling holes?

When you replace the pulls you can find ones that have the holes spaced the same distance. No drilling then! Take the old handle with you to the store.

PowerGrab might work

Take a photo or one of the drawers to the hardware store and ask their staff for recommendations....they may have products or solutions you never considered.

Cabinet knobs and pulls that slide on the edge of the cabinet are available. Some examples shown below.

Here's a video from someone who used Command hooks for cabinet knobs.

The more delicate looking clear hooks could also be used as knobs.

https://www.youtube.com/watch?v=ExucbGtyJUc