It's not the ideal time, but I don't think you'll do much harm. You might lose a few hydrangea and clematis flowers (depending on variety), but that's about all.
Detach as much as you can and just drape it over the border till you get the new fence panels in and can re-attach them.
Where you have to prune, make clean cuts just above leaf nodes to encourage new growth and reduce die back. Give everything a feed of tomato food which is low in nitrogen but high in potassium which will encourage new flowers but not sappy green growth which could get frost damaged as it won't have time to ripen before the autumn frosts.