I can not imagine why anyone would use MEKP instead of MEK substitute as a solvent or thinning resin. MEKP is a little scary and MEK substitute smells like almonds, is used to decaffeinate coffee and is less volatile then Acetone. It is similarly toxic to acetone though evaporates more slowly. White vinegar as suggested above is probably the least toxic.
MEKP is not used as a solvent or thinner. It is used as a catalyst for polyester and vinylester resins. It is an oxidizing agent used in very small volumes to make the resin harden.