From what i understand, you're taking a BIG risk by going to non-speciality that this person won't know much about transgender/transsexual issues and won't be able to write your letters.
If you found one knowledgeable and able, thats great! But i just came out to the folks and i would rather go to someone i KNOW is knowledgeable in the field so my parents have that to fall back on, than to someone who may spout mistruths or speculations.
At the best, a non-specialist will know enough to be able to help and will follow the guidelines for writing your letters. Second best they'll know enough to send you to see a specialist for further help. Worst case they won't know a thing and may "misdiagnose" you (which could be a disaster if the parents where there with you and grabbed onto that misdiagnosis like a lifeline.)