Cleanest way is to pick up one of these barrel connectors and connect your transformer wires to it (note they are marked for pos and neg. It should plug right in to the terminal section. They are available in a set of two male/two female for less than $4 on Amazon.
I doubt the black and red wires are soldered on. They should come right off the tabs with a hard pull with a set of pliers. You can then attach wires from your transformer to these female .110 crimps and push them on the tabs being careful to observe polarity. Also, available on Amazon.