I think they can shut it down. I dont think they can sustain it.They can mine the straight and threaten all traffic with the literal thousands of AshCMs and AshBMs hidden along the Southern Coastline in many underground bases, “missile cities”.
IRGC has built truly substantial infrastructure in the West and South of Iran solely dedicated to missile firing platforms.
The rest of the world (except russia possibly) cannot allow a regime that would do that continue to exist. It would be their death warrant..They havent built up enough to take on what would come to them. It wont just be NATO