I went through Dubai many times without a stamp in the passport. With Jet Aviation the crew were entered on the Gen Dec and Crew ID's (Which were made in house by our own company)
Just make sure you don't stay longer than the 7 days. Did that once and it was a lot of extra hassel.
"Why don't you want your passport stamped?"
Because you will soon run out of pages in your passport if you fly round the Africa or the Middle East much.
There was a company in Germany not long ago that would make up Air Crew ID Badges Credit Card style to your spec which seemed to work well. Can't remember their name at the moment.