You should check your hunch against the reality, at least periodically. The US dollar has strengthened since the current US-Iran conflict started.
I have checked. It’s too early to tell but anyway relative price is not what matters. What matters is purchasing power. EUR purchasing power was better and improving compared to USD. And check out interest rate derivatives — the euro has actually overtaken the dollar as the #1 currency in this massive market.
Yes it tends to strengthen during times of conflict as countries buy more dollars in response. That's kinda the whole gimmick with the petrodollar. War is good for the US
But if Iran does successfully force countries to stop using the petrodollar by only allowing countries trading in yuan through the strait, then we could actually see that reverse. IMO destroying the petrodollar is the primary clear "victory" Iran could achieve from this war