For cashmere, I would not try and unravel like that. It is already cloth, so I would use it in its cloth form. If you cut pieces out of it in its present form, you will need to finish the edges right away so it does not unravel, over cast by hand, zig-zag the edges with a sewing machine after you cut out the shapes you want. The other way to use the fabric is to wash the sweater to shrink it and felt it, then it will not unravel when you cut it. It will be thicker and warmer, but smaller available area of cloth. The felting way is most common, and easiest. It is also nice as ou can just hand sew the cloth when you
reuse as you dont need to worry about unravelling.
Use the cloth by either saving up to patch work a larger item later, or make smaller items now. Good choices for smaller items would be to make a hat or fingerless gloves or mittens or wrist warmers or a scarf to keep your neck warm. This will all be MUCH faster than unravelling and reknitting. Plus, as you can see, this thinner
thread sticks to itself and breaks easily. Unravelling a sweater with thicker yarn is easy.
A book I have on my shelf, Sewing Green by Betz White has a section with a pattern to reuse a cashmere sweater to make a baby hat and her instructions are to cut the sleeves off and cut them open, machine wash all, the sweater body and sleeves in
hot water with detergent. And to machine dry on a low setting to partially shrink, felted
enough to work with and not unravel but still soft and pliable. She instructs people machine sew with 1/4 inch seams, but you could also hand sew.