What mod chip are you putting in? If it is a wiikey, then you can do the quick solder method, but if you are doing any d2c mod, then you are going to need some wire (I have heard 30 gauge is the best). Also, that solder looks a little thick, but as long as you are careful then you shouldn't have any problems.
By the way, if this is your first time soldering I would definitely practice on some other stuff first. You don't want to go strait to the wii or there will most likely be a lot of errors.