I don't understand how feeling like you're in the wrong body manifests as suffering. If I woke up as someone or something other than what I feel like I am, I would react positively or negatively on a case by case basis. Whether my self-image matched my body would not be at all relevant.
If you were transformed into a being with no sexual characteristics at all, say, a magical non-anthropomorphic helium balloon, would you expect your suffering to be abated or partially abated or unchanged?
Attaching the label "me" to the image I see in the mirror is essentially all I do when thinking of myself as my body. What are you doing apart from that?
I assume you meant the wound thing as an example of irreducibly simple suffering, but actually I've spent quite some time investigating things of this kind through meditation, and they do break down further, in ways that make them much easier to deal with. In fact, physical pain is one of the forms of suffering most amenable to this.
What I was trying to get at with the balloon question is are you troubled by your body being gender A, or by it not being gender B? Is it an aversion, or a desire, or a restlessness, or what?