Replacement Handle Set With Exterior Keyed Lock

I have a Glass Sliding Door, and I need a Handle Set with an Exterior Keyed Lock. I am sending photos of the door as well as the hardware that is to be replaced. Following are the pertinent dimensions. (The photos may need to be rotated clockwise.)

The door has a rectangular hole cut out of the right (viewed from inside) frame. The hole is 7 1/8" High and ¾? Wide.

The door thickness is 1".

The door also has a square hole cut out of the edge of the right (viewed from inside) frame (for the Keeper). The hole is ¾" High and ¾" Wide.

The bottom of the Handle Set's Inside Plate is 1 ¾" below the bottom of the hole for the Keeper.

The Interior and Exterior Plates of the Handle Set are 7 ¼" High and 7/8" Wide.

Can you please tell me what to purchase?

Thank you.

I think Swisco Product Code: 82-002WK would work. Your website shows a picture with the measurement of the height (7 ¼?). What is the width?