Hi Alkay, don't worry too much about timbermate in the pup cavities, you should be able to remove most of it with a narrow paint scraper, chisel or large flat screwdriver. I usually leave a bit of TM residue and just line the cavities with copper shielding. Next build maybe mask tape off the cavities as it does tend to go everywhere !

As Waz says be careful not to do any damage to the veneer