There is another theory on why the F-19 designation was skipped, and why the USAF chose to use the rather confusing and nonsensical F-117 designation for the Nighthawk.
The theory is found in Tom Clancy's non-fiction book "Fighter Wing". In short, it goes on about how a US Air Force general in charge of the stealth fighter project found out about a plastic model kit named "F-19 Stealth Fighter Frisbee". The kit in question was released by US model kit maker Testor in 1986 and sold like there was no tomorrow. In fact, it is claimed to be the highest selling model kit in model kit history.
This particular general was fuming about it.
In order to have the last word, the general pulled all the strings he could and had the official designation changed from F-19 to the completely random F-117. So when the Nighthawk was shown to the public for the first time in 1988, its designation had changed somewhat.
This is of course just another rumour which happened to be heard and chronicled by Tom Clancy while researching "Fighter Wing". There's probably a fighter jock somewhere still laughing about it.