As far as I am aware it's only light and heavy attacks that trigger weapon effects + enchantments. For instance; Biting Jabs, although a Melee damaging skill, does not proc my Absorb Stamina enchantment on my Maul. It's a very valid tactic if you want to run the Axes but you should assume that you need to be weaving in regular light attacks between skills to apply it.

Now this doesn't mean I'm correct, someone else may have tested it more extensively and melee skills may apply proc effects, but get into the groove of weaving in light attacks anyway. Also stick some fire enchants on your weapons if you haven't already. The fire DoT from the light attacks will provide double the chance of proc'ing Valkyn Skoria. Or perhaps 1 axe with fire and 1 with disease for the heal debuff.

Thanks for the advice. Maybe I'll just run some tests with it and see how it goes. As for Valkyn Skoria in pvp for mDK it's very good err at least I really enjoy it. I swap between that and Bloodspawn. Both work great.