There's a wide variety of diseases which can cross species. There are methods of handling the animals which protects humans. Saltwater tanks are endemic with the bacteria that cause human marine tuberculosis (not the same as regular TB), but using gloves, taking care with open wounds, etc, makes it unlikely that someone's going to pick it up. Most serious diseases in humans crossed over from domestic mammals many years ago--and this still happens under certain conditions. So, technically, interacting with any sort of wild stock is not 100% safe. But, with care and knowledge, yes, it can be done safely. Protocols for handling animals, specifically sturgeon, are very specific in preventing the spread of disease not just animal to animal, but also to humans.