Welcome, puddin! Cute name!
You should be fine using cones, just make sure you clarify once a month. Unless the conditioner you use contains nothing but cones, and cones are all at the top of the list, there shouldn't be a problem
A lot of the people in the co washing challenge (including me) co wash daily or every other day with conditioners that contain cones. We just make sure to clarify once a month or as needed