Ships aren't going up there in this century.
If you go through UAE (the narrow part) you are attempting to build a canal through mountains and desert.
Any other route (the non narrow parts) would just be 3-4x the length of the Suez Canal but through a desert, but since its not sea level the whole way, with locks (which means more water... again, desert), and at the end forces you through an even narrower strait at the end (Bab-el-Mandeb). The Houthis in Yemen have blasted Israeli-affiilated ships in that strait before, and they are Iran-backed.
The only viable passage would be through the center of Oman (no mountain here) but that would be a gigantic canal. And that wouldn't really solve the issue, as the Iranians could easily block the canal as long as it is within reach of their drones and ballistic missile: you just need to hit one ship in the canal to effectively block it.