Are you spearfishing? If so, I think its extremely important to carry a knife. In fact, if I forgot to bring my knife on the boat, I just might not go in the water.
Besides fishing line, I am more worried about being tangled in my own reel line or shooting line after shooting a big fish. And in SoCal, this is complicated even more by the fact that our lines get wrapped all around the kelp, and we are down there, often in the murk, trying to cut the line and fish out of the kelp.
I want instant access to my knife, so I keep it on my left forearm where I can see it and grab it quickly.
And I think its essential to have a wrist lanyard, preferably bungee cord, so that if I drop the knife, I don't lose it. Dropping a knife can be fatal for a freediver if he really needs the knife. I run my hand through the loop of bungee before I pull the knife from the sheath.
The wrist lanyard also permits me to just drop the knife and let it dangle rather than wasting precious breath putting it back in the sheath when I'm through with it.
This is a bit specific to SoCal, but often I dive with the knife in hand to cut a fish out of the kelp. At some point I want to quit cutting and use both hands to grab the fish. I can just drop it and let it dangle from my wrist rather than taking time to put it back in the sheath.
The knife I use is an imitation of the Riffe, made in the same factory in Italy but without the Riffe name on it, and bringing the price down to only $30. There are other similar knives made under different brand names in the same factory.
And even though you didn't ask, I think the serrated portion of the blade is very important. When Riffe first came out with his knife, he did a demonstation for me in his shop (I happen to live just a few miles away). He put one end of a 3/32" stainless steel cable in a vise and held the other end tight with vice grips and had me slash at it with the serrated portion of the knife. It cut it in one try, but I always had my doubts that this was relevant to actual diving conditions.
But some months later, I had occasion to cut a 3/32" slip tip cable, in the water under actual diving conditions. It took two or three slashes, but I was able to cut it when I really needed to.