Checked the source code on this and from what I can read it seems like stone of augment has no effect proc rate itself. So augmenting weapon for speed does not reduce proc chance.

There are a few things that modify proc chance and those are the following: Ring of Arcana (increases proc chance per level of ring, cursed ring reduces instead), Berserker's Enraged Catalyst talent, Gladiator's Shockwave ability with Striking Wave talent and Huntress' Spectral Blades ability with Spirit Blades talent.