I don't know how it works in your country, but in the UK, a therapist will list a number of issues they're skilled at working with, not necessarily highlighting one of them. So you may find someone who has experience working with gender issues, but doesn't put that at the top of their list on their brochure or website or whatever. The therapists know they're dealing with clients who need discretion, so it's at least worth looking for someone like that who's not so obvious.
The therapist I'm hoping to see when I move has a whole big list of things on her website, like anxiety, depression, etc. etc. and gender issues is just down there somewhere in the list. I just know she's good with gender issues because I found her through a website that deals with this. So maybe your first port of call would be to find a website that gives support and advice on trans issues in your country, and look for therapists through that, and then see who's nearby whose publicity/website doesn't give the game away for you.
Sorry, I'm getting into "man giving advice" mode here! - I do understand that you're really worried about your family finding out before you're ready to tell them, I hope this is helpful.