Do like the native people did, go with what you have, or trade for better stuff.
You won't find anything sharper than obsidian, but you have to treat it like glass. Uh......because it essentially is. Make it a little thicker, and shorter. Any stone blade is going to be somewhat fragile, compared to a steel one. Even Rhyolite. Though it is tough stuff as every one here seems to assert, it is not steel. Like they said, stone knives were not for throwing, stabbing, (except in emergencies) or prying with. It was a cutting instrument. You have a lot of material choices. Experiment with different types of stone, and see which one suits your particular needs, and holds up to your type of usage.
I wouldn't know. I never made a knife. I am ecstatic when I make an arrow head, that is not a bird point, or granules for the debbage pile.
Wayne