Oops, your right. I miss read the tooltips. In that case the first solution I can think of off the top of my head is to make skill cooldowns/costs adjust based on weapon speed. So if you've got a fast weapon then you can activate skills more often at less of a cost. Slower weapons increase the cooldown and cost to make up for the increased damage.
edit: Or it could be balanced by weapons having lots of % chances to proc effects, which faster weapons would be much better at.
