If you use the dictionary definition of "exotic" (strikingly, excitingly, or mysteriously different or unusual), I would offer the Kriss .45 pistol.
The vector operating system (recoil reduction) is unlike anything else that I have ever shot. I find one hand shooting of the Kriss produces less recoil than I get with my 7.63 or 9mm broomhandles.
As far as exotic looks go, it's 19th Century vs 21st Century (you love it or you hate it).
Mark