Long post:
I'm not presuming your knowledge or ignorance.
The recurve/hawksbill/kerambit style blade may have been developed in a number of places, without influence from the others.
The history I read concerns it's use in the Philippines, where it was developed in response to the needs of a fishing culture. Much of the utility work involved cutting rope, and the recurve made it easier to do this, by allowing the blade to stay centered on the rope. The pommel ring is assumed to have begun as a handy way to keep the knife from falling over the side, and allowing the use of the other fingers without having to re-sheath the knife.
As with many utility tools, it was adapted for fighting on an as-needed basis. Somehow, this developed into the formalized martial art now known as Escrima, Arnis, and a couple other names.
The recurve knives you see today are mainly intended to be used within the structure of these knife-based combative systems. An example is this one, by Emerson:
As I understand it, Ernie Emerson is trained in Arnis, or something similar.
These knives rarely top the 3" limit. To the best of my knowledge, the only production folder with a recurve blade over 3" is the already-mentioned Spyderco Civilian:
I cannot cite a source, but I have read that the Civilian was intended for use by untrained people (ie: civilians) as a last-ditch weapon that would do considerable damage to an opponent, even if the user was simply flailing the knife in a panic.
The question of whether or not someone under such duress would remember to use their knife is unknown.
The Civilian is only available with a fully serrated blade, although you could grind off the serrations.
With the proper training, recurve blades are fast and effective deterrent measures. Now I'm not presuming anything about your level of training, but without some practice time, the recurve knife is not as effective, as, say, kicking a fella in the groin.
My point is: the size and shape of the blade is actually less important than the amount of time you are willing to invest in learning how to use it effectively. Take it for what it's worth.