How do you hold the wound shut, hold the thread in place, and apply glue all at the same time without getting the glue everywhere, especially over the hand holding the thread?

I always just use a single-ply piece of paper tissue, and soak that in the glue. It's too thin to hold much glue, so it doesn't get that hot - if you need more strength, you can add more layers. And it can be applied one handed - place tissue over wound and apply glue. Done.