Honestly, I don't think it's a bad thing at all that you're considering your dating range; many people are indeed attracted to people who have penises but look or seem like women. A lot of people. But your choice from here probably really depends most on the pattern of the partners you date. Do you find that the people who enjoy your contradicting parts tend to be the 'right' people for you? Do you usually like these mens' personalities, looks, and lifestyles, or do these men tend to be different from what you prefer as a woman? Have you had more bad experiences when telling men the nature of your parts, or have more people appreciated it than not?
I would say that the common pattern among the folks who are attracted to you is probably that they are gay men who are searching for womanly aspects in a partner's personality and facial qualities; if you feel that any of these men are "too gay" for you (as in usually too female acting themselves, or "not straight acting enough"), it may be time for you to undergo SRS altogether and fully transition into a woman. There really is usually a big difference in personality between the men who like penis and the men who like vagina, it's no stereotype based on my experience. If you plan on being in stealth mode, I would say SRS could open many, many doors in the confidence and dating department.
For me personally, I think my first step is to get where you're at; female in appearance so that I can simply socialize and date a bit more. Quite frankly, if I at least look like a woman and act like a woman, (and I have no shame in saying this:) then it truly can open doors for me concerning how I enjoy giving oral sex. I could truly have many quick-sex partners just by giving oral sex, no showing of my true genitalia required. But a womanly face and pressence is a must for the very straight-acting guys I'm attracted to, and want to have quick dates, quick social experiences, or quick sexual experiences with. It's not until a very long time after knowing someone or loving someone that I'd let them "do" me anyway, so just in speaking of quick sexual situations, a vagina is much less needed for me.