it is hard finding cone-free conditioners. I too suspect that cones were causing/contributing to my itchy scalp and hairline breakout problems. Since cutting out cones things have really improved.
I use gobs of conditioner, I like to finger-comb the conditioner through, and it takes lots! I have found a few cheap conditioners at WalMart that work for me.
I am now using Jhirmack EFA conditioner, it is kinda thick and smells great [like Orange Julius]. I also like Herbal Essence Clean Rinsing for Normal/Oily hair, it is thinner, but works well too.
Some of the Suaves have no cones. I can't remember any others off-hand. You could go to drugstore.com and research ingredients if it is a hassle reading bottles in the store [it is for me LOL].
I am also going to get Nexxus Humectress, I used this years ago, don't know why I stopped. My hair loved this stuff...
39/41.5/whatever!
Type 3a/b
AshBrown, more than a few Silvers...