If the cone isn't water soluble (which you could remove with cowashing), baking soda and ACV will not remove it. You can low poo with one that contains Cocamidopropyl Betaine if you don't want to jump straight to a sulfate shampoo. Cocamidopropyl Betaine will remove any and all silicones. If you choose to go with a sulfate shampoo, Suave Naturals are all silicone free (and cheap).
CG since 11/2011
2c /3a F /Mii, low porosity

Summer Products /Routine:
Clarifying: ACV rinses, Suave Professional Men Deep Clean Peppermint
Low Poo: Renpure Luxurious Argan Oil
Co-washes: VO5 Kiwi Lime Squeeze or Strawberries & Cream
RO: VO5 KLS or S&C, Cure Care
LI (if needed): VO5 S&C, VO5 SC, Cure Care
Stylers: FSG, AIF,
Tresemme Flawless Curls Bouncy Curls gel
PT: IAGirl's (link) as needed