No solder skills needed (nor recommended for things like harnesses, they should be modular to be removeable). All you need to do is pick up a crimp tool like this one
http://www.mcmelectronics.com/product/22-1795 and some 16 or 18 AWG quick disconnects and you're set. Crimper is a very easy to use tool and a necessity for this hobby, you can find them from anywhere between $10 and up.
The speaker does not connect to this at all. This only gives connection for 3 extra buttons per player and a extra ground wire per player, but you can just daisy chain from the other buttons for ground.