It would cost a bit more is the worst case if you had to build your own centerfuges, uranium is not all that rare. And a single ship could carry a decades worth of fuel (not that I recommend a decade of fuel on a single ship), so even if shipping was costly it would be cheap compared to the actual fuel refinement. You couldn't Hormuz a uranium fuel supply because it doesn't take thousands of ships or miles of pipeline to deliver.

So maybe not worry free, but if you are able to run nuclear reactors for power to start with, obtaining fuel for them in any scenario shouldn't be impossible. You got atleast a year or two lead time between refuelings, and it might be able to be stretched a little longer in an emergency. And even more time if you hold some in reserve.