Open your stapler flat, as if to use with a bulletin board. Fine a suitable substrate like cork or loose fabric or foam, for the staple to be able to push through the paper with staple legs remaining unbent.

Bend these staple legs over nice and flat, or beyond flat, just as would be done typically by the stapler's inegrated anvil.

As an additional safety or decorative measure, you might put a piece of tape over the snag-prone legs of the staples. By over-bending the staples, beyond flat, this step can be avoided. Washi or masking tape will work best to conform to the shape of the metal.