Gees, agreeing with Ric yet again.
Compressed air and a blower gun with a very long tube is my suggestion and what I use in the shop.
got them from 5' long ( yes a newie ) a couple of 4' then a dozen or so down to 6".
Long guns mean you can stand back so you don't get covered with clippings & dust.
Also you do not need to crawl under the mower or burn your fingers blowing around the engine.
Water on the top of the deck is a no no as it usually does not remove the grass very well and leaves clumps of wet grass sitting on your deck, rusting nice big holes or wicking under the powder coating.
Water under the deck is fine just so long as you leave the blade spinning till it dries off.
Air is good because it will shift accumulated grass from inside spindle covers.
Second best is a leaf blower but no where as good.
You should never ever turn up at a job with grass clippings on your machine.
Doing so will leave you wide open to accuations of spreading weeds to your customers property and it is not a good look.
Ditto with grass all over the trailer.
Clean machine, clean treads on tyres is a good look and convinces he customers you are looking after their best interests.
Cleaning your tyres will show up infestations of things like Bindi grass abd other nasties then you have the option of notifing the customer and getting an add on to spray for the offending weed.
Also cleaning off after each job means you will be taking a close look at your mower so will notice the missing bolt, bent blade, frayed belt, thornin tyre etc, long before it causes a failure.
Swapping out a belt with the mower on the loading ramps is a lot easier than pushing it 600 yards then trying to crawl under it sitting flat on the ground.