Ohio is a state where doctors can use the informed consent model, yes, but it can still be difficult to find a doctor who doesn't require a letter from a therapist. I've heard from other transguys locally that Dr. Dixon at University of Cincinnati Hospital (the Hoxworth Center, actually) doesn't require a letter
sometimes, but she wanted one from me (I already had it anyways, maybe if I'd have explained that I couldn't afford or didn't believe in therapy I could have gotten around it).
Unless you have good insurance though, it's still going to be expensive. I personally switched from Dixon to the Howard Brown Health Center in Chicago 6 hours away because Dixon's office billed the blood work with the transsexual codes that my plan excluded (many plans do).
http://www.transqueerwellness.org/Health-OhioOn the top half of that page is a list of primary care physicians in Ohio by city who might prescribe hormones with informed consent, there's never a guarantee though. These resources change frequently and people are often told different things by different receptionists.
I help organize a trans* community group in Cincinnati, and a bunch of our members just make the trip to Chicago a couple of times a year to go to Howard Brown because their staff treats people like humans and doesn't mess up anyone's name or pronouns, are very knowledgeable, offer sliding scale for those without insurance, and offer gynecological and primary care too, if needed. I found my experience with a general practitioner to be stressful by comparison.