I have an older hand climber too. The seat on a hand climber folds up quietly and easily, all you need is a bungie cord. I don't use the straps between the seat and platform portion, replacing it with a rope to prevent dropping the platform when going up or down.
Take a bungie about 12" - 18" long. Once you have the stand set in the tree, hook one end of the bungie around the seat platform belt on one side of the seat close to the tree, pull tight around the front of the tree (opposite side as the belt), go over/under the belt on the other side, and then tightly back and hook on the same side you started. This holds the seat firm against the tree, no slipping when you stand up and you can also fold the seat up against the tree when you want to stand. Works great, but I don't think you can do it if you use the stabilizing straps. I've never used, nor seen the use for them anyway.
The seat portion alone of my hand climber, along with the bungie cord, also makes a great seat for ground hunting if you have a tree to mount it to.