Just wondering do you have to complete any tests/provide any proof of being able to swim before you start work on board?
Not usually. I have heard of one safety training where people met at the pool onboard and had to right an overturned liferaft, but that was years ago. Those who couldn't swim had to wear lifejackets.
For some jobs, a SCUBA certificate is handy, but this is mostly marine (for looking under the ship), aquatics (teaching diving) and some of the new RCCL ships with the Aquatheaters (like stagehands in Cirque water shows).