You can use any willow for weaving, but some is very definitely better than others for doing so.
If you cut the branches, and stack them upright for a day or so, they'll strip a little easier.
If you use them 'green', as in fresh, then they will shrink, and that shinkage will loosen anything you make of them.
That's why we usually dry willow, and then re-soak it to make it pliable again before we use it.
If you dry it with the bark on, then it will take a lot longer to soak until it's pliable again. If you don't soak it long enough, it'll crack and split when you twist or bend it into place.
It's not unknown for it to need 48 hours soaking.
Commercially prepped willow has sometimes been steamed, and that stuff takes just a couple of hours to soak thoroughly.
Keep it damp while you work, an old towel soaked and wrung out works fine, or find someplace cool and damp to work.
I hope it's a success
and I'd love to see what you make of it
M