IME - and I've done both - it's often more economic to simply buy an aftermarket body in the preferred finish than it is to refin the existing body; for example a while back I bought a stunning new Warmoth 3tsb body for not a lot more than a refin had recently cost me, which was close to £400. OK it's most useful with Fenders/Fenderalikes and MMs of course but there's a 90% chance after all 👍