This is just an example of the kind of scissor I talk about all the time, but any small, curved, embroidery scissors will work for cutting tiny jump threads or loose threads on your embroidery designs.
I’ll be honest, I have this exact pair of embroidery scissors and they are not my favorite because the tip is TOO sharp and I’ve stabbed my fingers with them. So they are definitely sharp and they stay closed.
I also have this set which works well and the colors are pretty.
Or you can’t go wrong with a pair of Gingher scissors, these are super high quality: