Viagra is how they do it in porn despite hormones I remember reading at one point, and a quick search does show some mtfs using it. But absolutely do not skirt around your doctor to get Viagra, it is a bad idea to break the doctor-patient trust. Just have an honest discussion with them about why you want it, unless you have another condition it shouldn't matter at all with the HRT. If they still don't give you the prescription even if you accept the risks, and they don't have a good reason (being on two medicines is not a good enough reason if they have no interaction, "no more pills for you" is not good medicine) then maybe it's time to find another doctor.
I'm not sure how Viagra is metabolized though, so maybe your doctor is more concerned about liver issues.