I would guess that SLS (second ingredient) would get out just about anything, but it could dry your hair. Others may have recommendations for gentler shampoos that will still get out the cones.
Jessica
Type 2c: coarse, high-density, low porosity (so it would seem)
Avoiding protein and glycerin; going for soft, non-crunchy, frizz-free waves
CO & RO: Tresemme Naturals Moisture
Sealer: Olive oil
Leave-in/Styler: Kinky Curly Knot Today
DT: olive oil and honey