Ok, I tried to make a guide for you. Today I learned explaining things is not one of my talents. I made a pic related to go with it in the hopes they might make sense together.
There's a couple minorly different ways you could go about this but I stuck to one route for simplicity. Also I'm mostly self taught so if more pro anons want to correct me I won't be offended. If you're not familiar with stuff like types of stitches those have tons of really helpful guides with just a quick google, though I tried to illustrate ladder stitch.
1) Rip/cut the stitches of the wrist seam, so you remove the whole hand.
2) Take the stuffing out of the hand and put aside.
3) Rip the seam holding the hand together, so you now have 2 separate flat pieces.
4) Lay one piece on top of the other, soft sides facing each other (the sides that will be seen on the finished plush) with the edges lined up (they should easily mirror each other).
5) It's possible to do without, but most find it helpful to find a temporary way to hold the pieces together so they won't slide around while you sew and make your seam wonky. Usually it's done with pins. I find pinning can be frustrating with small pieces so you can also try other things, like small clips, or doing a few tack/basting stitches.
6) Sew all around the sides of the two pieces - except NOT the wrist sides - leaving just a small space from the very edge of the fabric (seam allowance). I would expect there to be small needle holes or at least creasing left from the original seams, if so you can use those as an easy guide for where to sew. If you're confident enough with the machine you can use that, but a hand sewn back stitch works just as well.
7) Turn it inside out, so now the soft sides are on the outside.