I'm rather sure that you need a wii remote to interact with the stock wii os to install the RVLoader, so you can't just use a gc controller until after you have already softmodded it.
Soldering a wire to the multi-out to get composite out is rather easy and should not present much issues as long as you can figure out which pin you are supposed to solder to from the guides like The Definitive Wii Trimming Guide.
The power is another issue though. I would say, if you are new and need to ask if it is possible, then no, you can not do that, and getting a normal charging brick is way cheaper and easier.
Longer explanation:
USB charging is finicky in that there is a lot of communication between the power brick and the receiver, as to what voltages both support and which should be used, and if that communication fails, the brick will default back to only supplying 5v at low amperage. So you would need a custom chip that can tell the Usb C PD to deliver exactly 12v (if your brick supports it), and support the amount of amperage that the wii needs. The normal RVL PD + PMS combo does not support 12v, so you could need a custom solution to just power on the wii. And making something custom just to handle that would be expensive and pointless.
There are other simpler ways to deliver 12v power, but I strongly recommend just getting a regular wii charging brick, unless you already have a good amount of experience in electronics and have things laying around, (beyond suggesting to use Type C PD to deliver 12v to power on the wii.)
