I'd prune the older growth out. wild roses are very large plants with long wavy stems, very painful as you've found. If they get up into trees they're quite hard to pull out when they die off which they do often. Naturally they make great thickets, a bit like bramble with dead stuff inside and live growing away. Not pretty for a garden.
Hack it back as much as you want-it will bounce back-probably quite painfully