Need sliding screen door handle with lock

My door is 30 years old and there are no markings on the HW. It is currently hanging on by the spring and lever. I watched your utube video and I think that 83-002 handle might suite my purposes. I am conderned about the width of my frame. My frame is 2", but the flat part is 1 3/4" where the handle will rest flat and the spring mechanism will need to reach. I dont mind drilling new holes to attach the handle onto the frame. My old handle had rivets holding it onto the lip of the frame which isnt very sturdy, and they broke off as you can see.
Please advise.

They are not screw holes, but rivets that are 2 3/4" apart (center to center). The handle was mounted on the inside edge of the door with rivets that eventually broke off. I dont think that another handle mounted this way is acceptable. My plan was to drill new holes.