The correct answer is 'can't'.
Here's why:
The sentence 'The water in the river isn't very cold, but you ______ swim' implies a situation where although the water isn't freezing, there's still a reason why someone might not be able to swim. The best option is 'can't' to mean you aren't allowed to swim.
* can't (can not) - Indicates a lack of ability or permission.
The other options don't fit as well:
* don't have - does not fit grammatically and does not reflect the meaning.
* shouldn't - means that swim is a bad idea, this is a moral suggestion.
* mustn't - this is a stricter version of 'shouldn't' that means swim is against the rules, but it does not fit in the context of 'the water in the river is not cold'
So, the complete sentence is:
The water in the river isn't very cold, but you can't swim. (Вода в реке не очень холодная, но тебе нельзя плавать.)