I think that shutting down the SOH is much harder than many expect, especially for a longer period of time. Not to mention the economic impact would be devastating on Iran itself and would cause significant domestic as well as international political problems.
I think they could halt movement through the SOH initially fairly easy. The SOH isn't very big and all they have to do is sink a couple tankers, causing others to get skittish and avoid the area. Insurance prices on ships going through there would probably sky rocket, making anyone who would still go through think twice. I agree though, sustaining it would be difficult for them however by then most of the damage would be done.