Your best bet would be to download a v1.02 .iso file of Melee, but I can't provide you with a link. It sort of invalidates your hard copy because that version of the game is incorrect. I'm not sure if you have a Wii that already has the homebrew channel, but there are tutorials out there if you don't know how to mod your Wii. Nintendont is the homebrew app that you want to download online to launch GameCube games (.iso files) on the Wii, provided that you have a decently sized SD Card/USB depending on how much you want to mod. In order for Nintendont to read your games, you have to create a folder on the root of the SD/USB called games (all lowercase), and a folder inside of that called GAME01 (Each folder that holds a game increments by one, so GAME02, GAME03, etc), and inside that folder holds the actual .iso file where you must rename it to "game" (without the quotations). It can be a hassle to do, but it does pay off.
You don't necessarily have to do this method especially if you can get it working on Dolphin, but you never specified what kind of GC Adapter (Mayflash, WiiU GC Adapter, etc) you have that doesn't work on Dolphin. I personally have no issues with the WiiU GC Adapter, but if that's the adapter that you have then there are tutorials on how to get it working on Dolphin. Although it uses 2 USB ports, you only have to plug in the black USB port if you don't care about the rumble, which is what the grey USB port is for.
