Hi,
Personally, if you have a second vac that has a blower port or an access to an air compressor, I'd try blowing it clean in reverse of the normal travel of air through it. This is not a job you should do indoors.
Attempting to wash and rinse it out sounds nice but but the machine cannot be safely used unless this part is thoroughly dry. I have no idea as to what constitutes SAFE drying time for this kind of thing unless it can be taken apart and therefore will not recommend it. The following link is your best bet. You can download a maintenance guide for your specific Dyson model.
http://www.dyson.com/support/default.asp
Good luck,
Venson