Look for 'Sorbothane' rubber. It the stuff they make the Olympic wrestling mats from. You can drop a raw egg on one from chest height and it won't break. It doesn't even bounce! It absorbs most of the impact.
Right now, the cheapest way to get Sorbothan in thin, flat small pieces is to buy "Spenco" brand shoe insoles. Costs about $10 and you can find it in many shoe stores and pharmacies. I've used these inside my shoes for years. I learned about them from a postal worker who walked miles every day. VERY effective. I've wrapped hammer handles and wood splitting mauls with it and it works great! There are MANY different insoles made from Sorbothane today, but 98% of them are contoured for the foot and cost about $30-$40. For wrapping, you need to find the thin flat ones that sell for $10.
Stitchawl