Talk to Goodwinch in Devon, David Bowyer will supply it by the metre with a hook spliced on, so you can buy whatever you need to suit the trailer length.
I have been using it for ten years now and have had zero issues and I cannot imagine a single reason why anybody would use anything else, either wire or those silly straps (and I have previously used both). I also use it on the hydraulic winch on my Defender and likewise wouldn't use anything else.
Mine is this stuff, though I didn't buy 15m, I only use about 7m on my drum, if you email them they will supply whatever length you want:
Dyneema® Bowrope 6mm x 15m - Goodwinch
I live under what's left of the hole in the ozone layer, and can confirm you don't particularly need to worry about UV light! In any case the 6mm is rated at 4,000kg whereas most straps are only about half that:
I simply fitted mine on both the winches I have used (both of which were very similar to your Fulton) by feeding it through the hole in the side of the winch drum where the strap retaining bolt went through, putting an M6 washer over the end of the rope, and tying a knot in it. If you do manage to cut or break it you can splice it fairly easily, which you can't do with a strap. But it really is fit and forget! If the drum doesn't already have a suitable hole, you can drill one (would need to be about 7mm).