I'm not entirely certain I know what kind of C02 cylinders you're talking about. Only ones I know of are those dinky little ones for air pistols and whatnot. That would make the 'mortar' rather tiny...
Static is right, however, on a few points.
...As long as you have a good fit (not snug, but slides easily and isn't sloppy) between round and tube, you
should have enough force behind it to expel the round with no problem.
... Make the fins longer, but the round
will have wobble regardless, especially with light rounds. Aiming with a good and 'serious' homemade mortar is hard enough, but the fins should help the little rounds flying right.
...If this device is as small as I'm picturing (for small CO2's), then Exnay the fuse. Sparks will be falling down the tube while you're trying to put the round in. I get great visuals in my 'minds eye' from that one...

Put a "touchhole" on the mortar tube for the fuse or you'll eventually lose a hand. Electrical ignition is a good compromise as well. Point is, you want some distance between you and the launch tube. Start off with
small BP charges at first; 'til you get a feel for what the tube can handle. It really doesn't take alot of powder to send 'em flying... Some might argue this point, but if you can't do it safely then why bother?
... I realize that the drawing is simple and exagerrated, but the firing pin (nail)/primer setup (as shown) is notorious for going off
immediateley if sufficient acceleration is applied to the round. That's with big rounds of a few pounds +, however, with serious acceleration issues... Dunno if you'd have that problem with a small CO2; if it's really light I would be surprised if the primer even went off if it landed nose first. On hardpack or concrete, maybe, but soft dirt?
Use a small, round, steel bearing rather than a nail.
Hope there was something helpful in there...