Okay, I'm really confused about the Rylai's...Volibear is in no way AP, he's AS with his main damage output coming from bonus HP.

Frozen Mallet would be much better, as it makes his attacks slow rather than his skills. It also gives him more bonus HP, and a small amount of AD, which is what you should be focusing on.

Shurelya's is good in every way, but Nashor's is once again a step in the wrong direction. Since you would already have 25% CDR without masteries and you have a massive amount of bonus HP, as well as Frenzy and runes giving you plenty of AS, I would go with Atma's for some extra damage.

AP Volibear doesn't work. =/

Runes should be: 3 Quints of Alacrity, 9 Marks of Alacrity, 9 Seals of Vitality, 9 Glyphs of Focus.

Suggestion. His AP ratio's aren't really that great. His Q has a 1:1 AD ratio and his W is a massive damage dealer. Since you want to proc his W often you want the AS like you've said. But I wouldn't bother with getting AP items. I would look for synergy between HP and AD items. I would get my AS from Runes and a single item ingame (for this I've looked for something that gives him something that synergizes with his W). My thought is a Black Cleaver because it gives good AS,AD,and a good passive. My other thought is a Ghostblade, it gives you CDR (his W has a real long cd even at lvl5) Armor Pen, AD, AS and movement speed (works well with you Q if you don't have Reverie). With runes, masteries, and a single item like that I don't feel like you need more AS and then I just build up HP and damage items, making sure to grab a frozen mallet for the sheer awesome it does with his W and then resistances if necessary.

I understand my guide is not completely done, but whilst im developing it the basic's of my guide are out and you can follow them, the indepth details will soon follow, and other details people request will be delivered, just let me know :)