Hello, I'm CaptainTimmy a Silver Jungler and I'm here to teach you an efficient ap warwick (not recommended for ranked XD).

-First Clear : First, start blue and go clear gromp and wolves. Start Q and tank for a bit and then Q. Continue either W Or E. I prefer E because it lets you with more life. Though with W you can clear faster(Note: don't use smite you don't need it). Then go red and clear it as fast as possible to early gank Top or Mid(if you are above than gold so your team aren't completely monkeys, tell bot lane to play safe because you ain't ganking there yet.).
Take first blood from Top or Mid or not and go to Recall with about 1000 gold that lets you buy stalkers blade and boots.

-Secondly : Go Red side and take raptors and crugs which will lead you to 5 level. Go then Blue side and take gromp and then go gank bot lane. Either you get them or not you will be level 6. At this time I suggest you farming because you have been ganking a lot. Of course if you find a juicy opportunity go for it.

-Middle to Late game : You have purchased Gun blade but you will see that you aren't that tanky and get killed easily so avoid going alone on tanky enemies. Once you buy a Spirit Visage or Rylai's go for fights. You will be like an assassin and your Q will do 300-600 AP damage to adc's and squishy targets.

-Late Game : You are kind of easy to kill on teamfights but a beast on 1v1, 2v2 and 3v3's.
Afterall this build is kinda crazy and I wouldn't really recommend it but you can have so mucj fun one shotting adc's :D.