Does Olaf fit the bill?

Olaf does not fit the bill. Perhaps I should be more clear: I would like to put together a set of champs which I could play by building AS/On hit & Tank (or AP) gear, but with little to no AD. Theoretically: Yes Irelia but no Jarvan. Yes Volibear but no Garen. Possibly WW, but no Olaf. Maybe Shyvana, maybe Skarner. Etc.

The presence of an attack speed increase in their skill set doesn't quite fit the bill. Nor is it enough to say AS because they're autoattack dependent. If these builds don't mix-max perfectly, I'm totally okay with that. But I do want to avoid building AD.