What other way?
Removing everything, putting new art on, then putting everything back.
You’d want to peel off the art before putting on new art, anyways. That way, it is sticking to the metal faceplate, and not some art that is already peeling off. And you’re going to have to take off the stick and buttons, anyways. But if you can operate a screwdriver, you’re qualified to do so. Just unscrew joystick, pop out pushbuttons, and remove and replace art. Then pop buttons back in (Or replace with Sanwa/Seimitsu buttons, this is a good time to do so), and re install joystick (Or replace). You don’t have to take out the PCB, barrier strips, etc. May want to take out the turbo panel and remove the faceplate so that you can use it as a cutting template. It’s not that hard to do. Won’t take too long to take apart and put back together.
Also, your use title says Fearless. You shouldn’t be afraid of this simple of a mod. XD
Guide for basically the full mod-http://pineconeattack.com/2009/08/06/how-to-mod-the-madcatz-fight-stick-with-seimitsu-parts/
Sanwa is the same process. May not require PCB to be rotated if you’re using the right joystick.