Super Mario Galaxy 2 will not break your Wii. The fact that it broke down when you got the game is just a coincidence, it would have happened with any game. It would be akin to thinking that putting gas in your car made it break down because you filled up just before your engine blew up.
Chances are you just have a dirty lens but it could also be misaligned, so a repair is the most thorough course of action. Once you get your Wii back you will be able to play SMG2 without any problem and it certainly won't 'break your Wii' again.
There is nothing about the SMG2 disk that is any different to any other disk. The only Wii games I know of that are different are SSBB, Metroid Prime Trilogy and Sakura Wars; because they are on dual layer DVDs which can be harder to read.
Just to clarify, I've played SMG 1 & SMG2 on 4 different Wii's (models ranging from 2006 to 2010) and not a single one of them has had any trouble with either game.