Re-screening question

Tech Question: I'm re-screening a sliding screen door. The handle was riveted to the frame. To access the spline & screen under the handle it meant drilling out the rivets to take off the outside half of the handle. Thought I would just remount the handle using nuts & bolts through the frame. No luck there as they got in the way of the latch travel. Drilled out the rivet on the latch lever so the whole thing is off. What handle would you recommend as a replacement? The old handle measured 3-1/4" X 2-1/4" with the mounting holes 2-5/8" apart [although they've been enlarged to accommodate the bolts I tried]. Would you have anything that does not require a pop-rivet as I do not have such a tool. Many thanks for your help.