I have a puppet that I needed the arms to disappear, so I put just a new layer in the arm swap group with a circle shape set to 0% opacity on that layer. That way the arms "disappear" to that 0% opacity layer and it appears to have nothing there when I swap to that layer. That might be a solution for you in regards to getting the original arms to check out.
This can actually be very hard to do because of some restrictions in CH. I would consider cheating. Have two puppets. The first puppet does not have a desk, so it can just walk around, including behind the desk. Then a second puppet is for when the puppet is sitting bend in the desk. Change the artwork so instead of "pants", put the "desk" artwork there. Then add pins and sticks so it does not move. Then its easy to put arms on top of desk. This requires you to hide the first puppet and desk and reveal the second puppet-and-desk. Or do a scene change. But its really hard to make the one puppet do both. (Not impossible, but really hard.)
The problem is a puppet cannot be behind and in front of another puppet (the desk) at the same time.