I do something similar to both free core and wood (moisture could weaken wood) handles on my rackets.
Being Canadian, I use one layer of water resistant clear hockey tape over the wood. Then i apply over that, 1 layer of regular black cloth hockey tape. For the Canadian's wondering, no i do not use "Howies" branded hockey tape, but i should ask for a sponsorship LOL =)

Good Alternative:
1) duct tape - very strong and waterproof and seems most common here in Canada for players that put towel grip over it as it's mess free removal.
If handles break often for you when playing this would likely be the most economical solution as your base setup for all rackets.