I think the stitches in a cut up sweater will fall apart a lot less than you think. Have you ever tried to undo a knit item to reuse the yarn. Very difficult. The stitches do not just fall apart at all.
I knit a sweater/jacket many years ago and found it was too big. So I sewed a line in the seam allowance right near where I intended to sew the new seam, then cut the extra knit stuff off and sewed the seam where I wanted it. I took the set (jacket and skirt) to the fair (open class) and got a second place ribbon.
I also know of many people who make mittens out of old sweaters by cutting out the shape of the hand and sewing two sides together. Beautiful mittens and very warm. Fair Isle sweaters are the most beautiful for this.
So, don't be afraid to cut up a sweater, especially after it has been washed in hot water. There is no way you are going to get that yarn to unravel even if you wanted to.