If you know the diver is male, say his right hand. That being said, sometimes you will see their referring back to a singular noun if the gender is unclear. Some prefer it to "his or her". Even though grammar rulebooks will tell one not to do this, there are attested examples of using 3rd person plurals (they/them/their) as a replacement for third person singular when the gender is unknown that go back hundreds of years.

Thank you Jeff and Michelle!

When the sex of the person is unclear or not known. It's assumed to be male. So, I would say HIS right hand would be correct. Although, if you said either one of these, one would know what you are asking.

It should be "One of the divers is holding a breathing device in his/her right hand." This is because only one diver was holding the device. The subject is singular.