in that case, instead of upgrading to nashors tooth you can just use the stinger.

just fyi Cooldown reduction hardcaps at 40% so with the 25% your getting from Nashors and the Heart your wasting the extra 10%

you're right about not having enough AP, and i was indeed unsure whether to add the phantom dancer or some more AP, and decided to go for it just because a teemo that has no attack speed is a sad teemo. however, buying something else instead of it would be totally acceptable and would not harm the purpose of the build.

You dont even have all that much AP. I would suggest getting a kage's pick early on for the extra gold, holding onto that for a while, followed by getting the soul stealer, then tear of the goddess, and then starting to upgrade your items into whatever you prefer first. Overall, your items should be similar to this in the end...
1. Boots
2. Archangel's staff
3. Deathfire Grasp
4. Z Ring
5. Soul Stealer
6. Nashor's Tooth
(can get these items in whatever order you prefer)
Back in the beta, I loved AP Teemo, it worked out great. At one point i had my shrooms doing well over 1000 damage, blind dart at about 800 damage, and my poison per second at something crazy like 90 per second. All this was with the Baron buff. Since then, AP Teemo has been nerfed, so dont expect to reach such results.