Passive healing pre-gunblade is negligible if you care enough to auto her or hit her with a spell every 9~4 seconds depending on her level.
The base healing that passive does is literally 3+2/lvl, at least up to level 11 where it changes, but you're normally out of lane by then. Akali won't be building enough AD/AP to heal over 70 in lane off scalings from her passive at a given time. It doesn't get anything substantial until she hits gunblade.
I can't say much about Doran's Shield because I don't build or face the item often, but she has 1 pot with Doran's shield. If you get aggressive enough to get her below half pre-6, she'll be in trouble.
I don't really feel like you're harassing her enough if she's constantly 60% HP pre-6, pre-gunblade, with Doran's shield start.