You are right, it is very likely not a simple screw shape at all. But if it can be removed without too much mayhem, it might be possible to drill through it and solder in a copper pipe that can be then connected to a (very expensive) valve, or pinched off as you say. Fortunately there's not much need to worry about virtual leaks in a positive-pressure system like this, so solder is likely O.K.
@lasersteve, I do imagine the gas would need to be sourced from some specialty company at upwards of $200 / bottle. I do not think it will be possible to bake the instrument too much though, as it is a permanent part of the camera assembly. Unfortunately it seems they glue these focal plane arrays to the cold finger!
For anyone familiar with these Ricor coolers, is this plug on top (image in first post) actually the fill port? Iif anyone has a broken cryocooler on this forum of similar construction, maybe we should tear it down

You would do well to look through the Thermal Imaging subforum. There are several threads relating to cyrocoolers. I believe Forum member Fraser has a good deal of experience with them. You might want to relocate your thread (or ask a mod to do it for you) to that subforum.
@gyro, thank you for the pointer. If there are any mods reading this thread, do feel free to move it to the thermal sub-forum.