I never play Akali, I've seen people build Guinsoo's on her - but usually relatively late when they are already snowballing I guess?
My Evelynn always rushes Rylai's (which is on-hit but not really what you mean), attack speed + Evelynn's AS Steroid make her AS capped
It's more about the AD+AP on her though, since her Q scales really well off hybrid items - also true of Hextech Gunblade.
I've never tried a hybrid Diana build actually - for ARAM I go full AP on her just so I can poke like a ranged (and shield well), for everything else though I go straight AD - which works out really nicely on Diana.