This is related to the other very interesting Kog thread.
Anyway, I think 20% AP on-hit is too much. If I were implementing this, I wouldn't go past 10%. However, this just doesn't make a lot of sense conceptually because he already has AP scaling on W. If they want to improve that, they could simply make it 1.25% per 100 AP etc. There is no need for a totally random additional on-hit with AP.
I don't think Kog (either version) is in a great spot now but the easiest and safest yet rather miniscule buff would be to restore the .7 AP ratio on Q. It's already a fairly easy to dodge skillshot. The other thing they could do is have the ult. bonus damage start at 75%, go to 100% at 11 and back to 125% at 16. This would keep his theme and identity intact while making his ult. more rewarding without it being overbearing early.