Of all the knife fights I have been in and seen, none of them have been decided based on edge cuts. I would recommend a knife you can stab with.
The first time I got jumped the dude had a shank, looked like it was made from a letter opener or something. He swung right for my head at full extension and I reflectively put my left hand out to stiffarm the blow. Well I caught the knife on the tip and it went handle deep. I still have very low temperature sensitivity in my left hand and my ring and little finger are at about 80% function over a decade later.
I got sliced up about a dozen times in one fight when I was a teen (I thought it was a fist fight, boy was I wrong). My sweatshirt was shredded almost instantly; fortunately none of the cuts made it past my ribs and the wounds were superficial.
Now I work in a jail and I have seen several shanks made by our resident craftsmen. They are all made for stabbing, simpler design, simpler deployment and easier to use in an ambush or a grapple. Damn near every knife fight ends up in a wrestling match, so bring the type of knife you want to wrestle with.
ETA:
These are the knives I actually use, I have at least one of them on me when I leave the house.
Top to bottom:
ESEE Izula II 2.63" blade for when I need a small fixed knife.
SOG Flash II Tanto 3.5" blade for when I need a folder
Buck 192 Vanguard 4.125" blade, it is about halfway between a skinner and a fighter.
SOG Seal Pup 4.75" blade mostly for utility
Also I would totally buy the Shivworks Clinch pick as it is very similar to the Izula II in size and based on profile it would probably be a better fighting knife.