slide heat shrink tubing over the connection to keep out moisture. Then rewrap with electrical tape. If you're not comfortable with soldering butt splice connectors will work. I used those over 10 years ago and have had no problem with the connection.
Also be sure to splice far enough back from the original connector to be clear of any green corrosion on the original wire. 2 or 3 inches should be fine.
You can get the connectors at conceptzperformance.com