There are all sorts of ways to protect wood from clamps. Unfortunately, most would be easier to accomplish if you had three hands.

Coat the business end of your clamps with the plastic-dip material marketed to coat tool handles. It dries to a soft, flexible coating that will protect even finished wood. Apply it by dipping or brushing, taking care to keep it out of movable joints or threads. Coat the grip end of a pair of pliers or locking pliers, too, to make a handy tool for pulling out wooden axle pegs and the like.
—Raymond Babcock, San Angelo, Texas