Open your stapler flat, as if to use with a bulletin board.  Find a piece of material like cork or loose fabric or foam, something safe to poke holes into.  Staple through the paper stack with the opened stapler, into this found piece of material.  The staple's legs should remain straight.

Next, turn over your booklet.  Bend the straight staple legs flat, or even curve the ends down into the paper beyond just flat (just as would be done typically by the stapler's integrated anvil).

As an additional safety or decorative measure, you can 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 should work well to conform over the ridge of the staple.