Can't you wash (and blow dry) the sheep before shearing? I know that legally it would still be classed as raw fleece, but it might help with some of the gunk... (I have a photo somewhere where my friend is shampooing a lamb in the sink for a photo shoot!)
Sounds ridiculous, but in fact it's what they used to do! We have a 'sheepwash' just below our farm entrance - the sheep would be sent across the 'wash' (pool in fast-flowing water, just deep enough to submerge a sheep) on a dry, blowy day, and sent out into the big meadow to be wind-dried. Then clipped the next day or so.
It won't remove the grease, though, and, much more relevantly, it won't remove any orf or other nasties either. You would have to get some detergent into the fleece for that.