True, that route goes through Kuwait and Saudi Arabia, but they could take a boat as well.
So communication and transportation is doable if they want to fight Israel and the "Great Satan" without the benefit of undersea cables.
Transportation of weapons to the Houthis would go to near zero if the Euros and others affected would put together a real coalition in numbers of warships, even small ships like the Coast Guard cutter we have in the area, to blockade everything but food going into Yemen. One DOESN’T need Arleigh-Burke class ships to do that, though a few more are likely needed to provide missile defense for the blockade.
Oh, and take out any Iranian intel ships for good. Capture might be best where possible (sort of a tit for tat, but just as effective as sinking them. Hell, re-man them including a few opposition Iranians and add to blockade.)