Thanks to Shag over at Firestorm Fan, I have this little screencap of what appears to be a Crime Syndicate version of Hawkman from the Justice League: Crisis on Two Earths OVA. Our Evil Winged Wonder appears on a screen featuring lots of evil versions of familiar heroes (you can see more here).
I wonder what the CSA version of Hawkman would be called? The modern version of the Crime Syndicate's Hawkman was called Blood Eagle, but I personally have always thought the name Raptor would be a good fit, too. (Much better than Blue Eagle, the Hawkman analogue from the Squadron Supreme!)
Evil Hawkgirl has a role in the film too, under the name Angelique.
I will have to track down a copy of this one, methinks!
Image: Crime Syndicate Hawkman, Justice League: Crisis on Two Earths, image retrieved from Firestorm Fan.