When I saw the substance abuse councilor because of my DUI, it wasn't bad at all. She was more focused on my mental health and trying to get me to ask for help (for anything), and to help me be less impulsive.
And the 12 step thing and religion were not mentioned at all some of the AA meetings I went to, so maybe this councilor can work with you without pressing those points, or making them obvious to you

I'm glad that you are open to the counseling. I hope that whomever you see is experienced in dual-diagnoses. I think that you will do well. You sound ready right now (((HUGS)))