The first thing that I thought of was an estrogen blocker and because estrogen is so crucial to getting and staying pregnant that without ANY, it's simply not possible.
Also, never, ever mix birth control pills and T. Cardiovascular events are extremely likely in that scenario (and they're already increased by the BCP's themselves) and so just don't even go there. It's risky enough just starting on the T with your own hormones initially fighting it. Synthetic hormones fighting synthetic hormones, forever? Even more risky. I don't feel as though my Endo was joking around when he told me that himself before my first shot... really.
I'd even be leery of the Progesterone-only contraceptives. If there's too much (which obviously there would be with the contraceptive methods using it) you would actually be increasing the estrogen rather than decreasing it (whether your own body's production, if it is still making its own, or else through the aromatase conversion of T to E).
But, there's virtually no risk at all of any negatives with E-blockers while on T. At least not anything that would be against what you said you were looking to avoid. But of course, you'd need to speak with a doctor (GYN or Endo).