Very few if any consumer market generators, especially open frame like yours are even water resistance. Water is not your friend, I would use first an air hose and air gun and then a terry cloth wiping rag.
Dust should only affect the air cleaner and the esthetics, clean is good but some dirt won't hurt.
IMNTBHO(in my never to be humble opinion)
"I travel not to go anywhere, but to go. I travel for travel's sake. The great affair is to go". R. L. Stevenson
David Bishop
2002 Winnebago Adventurer 32V
2009 GMC Canyon
Roadmaster 5000
BrakeBuddy Classic II