1) You have a few options. Either buy a bigger disc or modify the file downloaded using a program such as Wii ISO compressor. Before you do that, though, make sure you scrub the game using a program such as WiiScrubber
2) Soldering takes a tad longer and you have the risk of messing something up. Solderless is quicker, and if you made a mistake you can remove it. If you're out of Warranty or not putting a mod chip on your Wii will void it.