Yep. Straightforward job. You can get self adhesive copper screening tape off Amazon or eBay quite cheaply. RS Components do a decent sized roll for not too much money, too, if you want a bit more. You just need to unscrew and lift the scratchplate and stick it all over the inside of the body cavity (one layer is fine - no need to use yards of the stuff). Make sure it doesn't short against the jack terminals or any of the wiring. Remove the pots from the scratchplate and put a layer over the inside of the plate where it covers the body cavity. Then poke a hole for the pots and replace them. That will earth the pot bodies to the screening tape. It sounds as if your bridge is grounded already if the hum quietens when you touch the strings