Screen Door Lock replacement
Thanks for posting. There is a set screw near the base of the outside handle. Loosening this allows one to remove the handles and to re-orient them in the desired position. The video below goes into detail on this at raround 1:40. Let me know if you have other questions.
I'm sorry for overlooking that part of your post. I guess I'm not 100% sure what a latch nose is, in this case. Are you talking about the spring activated wedge that fits into the keeper?
If so, reversing these is very simply. You just push it into the mortise as far as it goes and then rotate it with your finger. I believe you also have to flip a little latch that's right next to it, which locks the wedge in one orientation.