As long as somebody who could could open up the case and put it back together and solder very fine points is available, I don't see why not.

You'll have to buy the part or parts from some online site. You have to know the exact model of your Wii as Sony kept changing specs everytime a hack was available. Anyway, you should be able to find that information on the Web too. There are some chips that come pre-installed on a special clip that clips on to the DVD player's electronic board and there's no need to solder anything. At the same time and place you can also get the special screwdriver that opens the case. It's cross-section is like the Mercedes logo, 3-winged.

After that, you'd need to find the Homebrew software for Wii and install it using a USB or SD card into the system.

Again, you should be able to find all the information on Wii or game hacking sites. Do a search for Wii Mod Chips.

Remember, hacking your Wii is legal since you paid for the machine and it belongs to you. It may (most probably will) void your warranty, though, if it's still under warranty. What is not legal in most countries that are signatories to the copyright agreements is the purchase and use of copied games. But you should be able to copy your own purchased discs and use the copy in order to safeguard the original.