can you regrow wild rose cutting without hormone
Rooting hormone is optional in any case, but you can make your own.
https://www.gardeningknowhow.com/ornamental/flowers/roses/roses-from-cuttings.htm
https://www.gardeningknowhow.com/ornamental/flowers/roses/growing-wild-rose-plants.htm
https://www.gardeningknowhow.com/garden-how-to/info/vinegar-rooting-hormone.htm
Zone2/3 Yellow climbing rose. 5 single petals. Needs no winter protection
It looks like a wild rose or species rose.
https://www.gardeningknowhow.com/ornamental/flowers/roses/growing-wild-rose-plants.htm
Now or wait until later in the fall? I live along the St Lawrence River.
I think that either time would be fine, since they aren't too particular about pruning. Most will come back just as strong, and will require this pruning to do so.
Here is an article that will help you to do so:
https://www.gardeningknowhow.com/ornamental/flowers/roses/pruning-roses.htm
Grows super fast with long runners entangling whatever it meets
They appear to be wild roses! Killing them requires constant pruning, and use of glyphosate, several times. It can take several years, still, to eradicate it in this fashion.
Here is an article from the PennState Extension that will help:
https://extension.psu.edu/multiflora-rose-management-in-grass-pastures-an-integrated-approach
You can contact your own local extension service, as well: