Speculating on how the US military could secure the Straights, one assumes the surface threat from any remaining naval vessels or skiffs etc would be relatively easily dealt with from the air with likes of Predator, Apache, fast air etc. Drones would be a little more problematic given their size and ease of launch; one would imagine every building in Bander Abbas and beyond could be abase to store & potentially launch them (is the US planning to level the city?). Ballistic missiles I would contend are less of a threat unless they have some form of terminal guidance, which someone here has reported that some do. Given the relatively narrowness of the passageway artillery (tube & rocket) could also pose a problem, but unless the Iranians are super-adept at shoot & scoot this could again be dealt with from the air with relative ease.
The big threat I see is anything subsea, be it mines or UUVs. Sure, the USN could send minesweepers into the sea-way to clear a passage however these would be a prime target for the Iranians.
(Sort of related question: does anyone know if any US or western warships have transited the Straights since hostilities began, also are any still present in the Persian Gulf?)