No it wouldn't. In standard speedsolving you are allowed the use of only the surface. One handed regulations should emulate the 2h regs, sans one of your hands. The procedure for a one-handed person's solves during the OH event should mirror those of their solves in the regular 2H event. This is even supported by the current regulations: "C1) Standard procedure is followed as described in Article A (Speed Solving)."
"C1b) During the solve no other body part or any object other than the surface must touch the puzzle. Penalty: disqualification of the solve. " is basically redundant, as it is already covered by the application of C1 on to "A5b) While inspecting or solving the puzzle, the competitor must not have any assistance from anyone or any object (other than the surface). Penalty: disqualification of the solve."
Without the superfluous regulation, the OH regs can exactly be summed up as "Same as 2-handed solving, but you can't touch the puzzle with one of your hands while the timer is running."
Edit: @fatboyxpc: That depends on your interpretation of "any object" in A5b. I believe other body parts falls under the category of "any object," and should be a DNF, with the theoretical exception of someone with no arms etc.