To the top of the z-axis motor it is about 45 inches (on my set-up).
Since I have the machine torch, that cable is somewhat inflexible and you would not want to bend it down too much so it would require clearance of about 54 inches. The torch can be removed, which is a bit more work and that would get you down to the 45 inch height.
If I were in your situation, I would install a magnetic torch mount. Then that would be a simple process. Personally, I would not like needing to unscrew the cap screws and dismount and then need to re-mount the torch every time I used the machine.
Here is an example:
Or if you have access to a 3D printer you could fabricate something:
Edit (more breakaway designs):
One that could be adapted or used with the others:
