Paul, As Larry mentioned, splicing dyneema is simple. MUCH easier than double braid. You don't need any special tools other than a very sharp knife. To pull the dyneema through you can just grab any small diameter wire, bend it, and use it to grab and pull.
Premium Ropes has some videos here on how to do it. If your line is on the winch then you would use the technique for an eye splice when one end is attached.
Instruction videos splicing techniques