The older models need access from the inside to relase a bracket that is screwed down to hold the handle onto the outer skin. There should be a few access holes in the inner sheet metal to give you an idea of where to look.
Very interested in follow up to this question. One of my sliding door exterior handles is loose. Still functioning for now, but I'd like to replace it if possible
I have a broken rear sliding door handle and I am currently looking to replace. I am wondering since looking at the part and the diagrams if the 1 bolt that rides along the inside of the edge of the door can be removed and then the whole thing comes out? I am hoping that is the case and may just buy a new one and hope it is that easy. If not I'll tear the panel off and go inside to do it. If I do it and remember I will post my results. I cannot find this info anywhere.