Having played the mod for a little while I have to say that a sprint button wouldn't really fit. The fact that you are slower and a speciman who is marginally faster can catch up with you if you don't kill it first is a very important aspect of the game.
So regardless of the knife-run vs sprint discussion I'd have to vote NO on sprinting if there were a poll.
The speed-boost for the knife could theoretically be taken out without doing a lot of damage but the knife would have to be improved then somehow, because as it is the speed-boost you get is almost too small to really make the knife a viable weapon anyway. Taking this away makes it totally useless.
I am against having to switch to the knife to run faster because it reeks of Counterstrike and regardless of your little "spoon strapped to your back, box in hand" experiements I still think it's unrealistic and doesn't make any sense.
Knife in a pocket or knife in hand makes absolutely no difference!
This leaves the weapon in hand vs weapon on back factor and here I have to say it's even easier to run with it in hand than having it dangle on your back!
Not that this would have any noticable impact on speed! Remember we are just jogging at most and "sprinting" (be it by selecting the knife or holding the sprint button) wouldn't be more than a slightly faster jogg. And I think a trained soldier can pull that off easily regardless of what weapon he is carrying! We aren't running top-speed in-game at any time.
There is quite a bit of a buffer between "sprinting" (via knife or button) to actually sprinting as fast as possible, and that buffer makes any discussion about whether an item is easier to carry in hand, on back, between legs, on the head, etc. null and void.
What we have to decide are two seperate things:
a) do we want a sprint button even though it goes a little against the philosophy of the game(, imo)?
pro: feels natural to be able to run a little faster from time to time
contra: takes away from the thrill of being chased and overwhelmed
b) how do we want to make the knife usefull?
speed-boost (this is what we currently have in the mod); more stunning power; knockback; magnetic attack ala Halo 2 sword but not as strong, obviously; poisoned so it does more damage overall but you still can't one-hit a specimen and you have to back-off so he can't retaliate; certain sweet spots for the knife only, where you can do extra damage if you hit them (throat, heart or whatever) etc. pp.