The outside of the transom doesn't bear any weight of the transom nor does it have much to do with the flex of the transom because of torque of the motor. However it does lend some support to the eye bolts and the gunnel. I've rebuilt numerous transoms and some that were much worse than yours.
Having said that, the fact that you do have rot in your transom only means that you're on borrowed time. How much, hard to say. Take a 1/4" drill bit and drill into the transom near the motor mounts. Don't drill all the way through, but into the wood a good bit. Check the shavings. Are they clean or are the dirty/dark, indicating rot. Are they wet? These clues will help you to know how bad it really is. If it is wet, its only a matter of time before it rots. If it is dirty/dark the rot has already started. Remember, rot is just a bacterial break down of the wood. Once it is wet, it starts. Once the rot starts, it continues.
As far as the cap. I've not seen one that was welded to the hull or the inner skin. You should be able to remove the entire cap as one piece and be able to remove the transom from there.
Can you take a close up pic of the area of concern? You should have an outer skin of the hull with your transom wood and then have a cap over it that should come off. It may be riveted, screwed or have some silicone on it. Some boats even have an inner skin.