Oh, please ....
You want to play that silly game then play it with the erection and operation of a gallows. And be honest when you do it. Don’t forget to include PPE for blood-borne pathogens when the condemned person’s head gets ripped off.
Your introducton of the erection and operation of a gallows indicates you agree that the nitrogen gas execution is not simple, but that the complexity is the same or less than hanging. Otherwise, why bring it up?!
My previous reference to the use of a rope in hanging could be done by the rope attached to a tree, a relatively simple method. A more formal hanging would add the complexity of a gallows. However there are procedures already developed for hanging, e.g., Procedure for Military Execution (Department of the Army, Washington, DC, No. 27-4, 1947). These include the length of the drop based on weight so that the head does not separate.
There are also various types of gallows, such as described here. The construction is not difficult for a professional carpenter..