Well, mine is welded on to the radiator so doesn't come off. And I just don't know about how it 'should' be attached so won't be of much help there.
I should have mentioned before that I was taking off a worn out Flexi-fan and installing a new Derale flex fan, both of which may or may not have more room between the fan blades for a guy to get an arm in there. From the looks of the stock Willys fan, there may be less room but I don't have first hand experience taking off the stock fan.
I will say that if your radiator is a bottom mount, they are pretty easy to R&R, and just leave that shroud alone. I have no experience with the side-mount radiator. Sorry, not much help here. Hopefully somebody who knows these things will chime in!