if you're going AP warwick you commit, don't try that many hybrid builds unless you know the champ scales well with both, I'm also pretty sure crit doesn't build well at all especially since you've just built AP you won't be using basic attacks without your W much.
It'll mostly be your ult and Q that do the damage so what's the point in going for crits if they don't do as much damage as your Q/ ult? Your build pretty much leads us to go for damage over time with like little pecks rather than getting the guy down in 3-4 hits.
Tl; dr: Crit warwick is the worst idea especially if you pair it with AP.