Are you suggesting that if Ukraine let go of the Russian-speaking parts of Ukraine that Russia occupies, people living in those areas would flee, or that people would flee Ukraine proper in the event of peace?
Neither scenario makes sense to me, why would you expect more people would leave if the bombs stopped?
They will be in fear if Ukraine rules over them too, there was no shortage of war-crimes being committed against the civilians before the 2022 invasion.
But in either scenario, they will be in less fear than if they’re literally being shelled.