VO5 conditioners are mostly all CG, I jhavent used them in a while, but when I was first starting out, I used VO5 Tea Therapy Clairifying Conditioner to co-wash, and another, more moisturizing conditioner to rinse out. Suave 'Professionals' has cones I think, the Naturals does not. But again, you need to always check ingredients. Memorize "-cone, -conol, and -xane" as ingredients to avoid. Mineral Oil and Petrolatum should also be avoided if youre not shampooing.
Tresemee Naturals is fine, I'm pretty positive it even says 'Silicone Free' on the front of the bottle. But dont forget, you need to do a silicone free sulfate shampoo again, otherwise this routine just wont work.
ETA: If yuou cant return the conditioner, silicone-y conditioners make GREAT shaving lotions! No need for it to go to waste!