How do 'big' sheep farmers get theirs to look so clean and white they can't surely wash them individually, suppose they must have a dip or something? maybe they have a big wetroom and stick them in there under the shower.
Well, this 450-500 lambs per annum farmer does not wash the sheep, no, and does present them clean and dry at market or abattoir, yes.
Keeping them wormed, fluked, mineralled, on the right ground and a little bit of cake helps. Dagging when dirty, keeping on top of any foot problems. Dag and bellies clipped before loading. Inside on straw the night before travel if they're wet or loose. If not in overnight, hunger, on straw or clean concrete, for a couple of hours before loading (so they don't make the trailer floor wet and mucky and then get that all over themselves.) (If hungering on concrete, keep an eye so they don't lie in their own wee and poo.)
We also have, over the years, evolved ways of handling them that minimise the amount of jumping over each other and generally spreading whatever wet dirtiness they can find all about the whole batch.

Plus, the majority of our lambs have 'tight skins', which is a big help. The water and muck doesn't stick so badly to this type of fleece as it would to something more shaggy.
Now, in terms of preparation of
show sheep, that would be a whole different story. And showering / dipping, washing faces with weak solution of Daz, combing, you name it, it all happens!

(But not on this farm, we don't show our sheep now.)