Assuming your ski has the carbon type dirveshaft seal (as opposed to the older style sealed carrier bearing driveshaft seal), running time should be kept to a minimum to avoid overheating the carbon seal despite having cooling water for the engine and exhaust. To avoid overheating the carbon seal.
There are ways around this but for my purposes I don't consider the option. I rarely use a hose to run mine on the trailer b/c I keep the running time to about 30 seconds, just as a quick test prior to launching to confirm engine will start and run normally
If yours has the carbon type seal and you must run longer, consider either a water spray bottle for lubricating the carbon type seal, or release the tension against the bellows to keep your carbon piece and rubber bellows happy.