Does anyone repurpose old knit blankets?

I have a knit baby blanket from when my brother was born. It’s been almost 31 years and now he is a father. The blanket is thin(ish) soft cotton yarn and is in good shape, with only one or two snags. It is really more of a throw.

I’d love to turn half of the blanket into a winter cap or a beret for myself, and the other half into an actual baby blanket or something as a gift for my brother.

Is this possible? Are there people or websites out there? I lack any sewing ability. We had a rough childhood, so my brother is more like a brother/child/best friend, and selfishly I would love to keep part of it. I would also be open to any other recommendations!