Heart rate while swimming

So i started back swimming and heart rate is fine. But if i want to wear a chest strap (I have a polar h10 and a viva from 4iiii), will it switch to external hr or do i have to disable the wrist hr while swimming.

Now, when i use the wrist hr, it records continuously. If i use a chest strap, i assume bluetooth does not work under water. So at the end of my swim, does any of the mentioned strap cumulate data to be downloaded to the watch or do i need the garmin swim strap ?