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Damage a ship, or maybe two? Before the harbour is cleared by Russian divers. Not at all a bad idea if the Ukrainians have the means. But it will in no way make the harbour unusable.
What kind of armaments do you imagine Ukraine having that could make a harbour unusable? 
They might be able to take out a few warehouses, maybe a bit of rail or if they hit the harbour with everything they have a pier.
You need some serious tonnage to make a harbour unusable. Like nuke scale tonnage and even that would probably only make the harbour unusable due to radiation. It's like trying to sink a piece of land. >

Send in divers and plant mines?