Something to cover handle holes?

Replacing broken handles on a two sliding panel shower. Original handles had a towel bar, which is now out of style. So replacing with simple handles. The 10-126 looks to work to replace on the outer side frames. (My door appears to be 1/2" width, so hope that is not an issue)

Any product to cover the holes on the overlaping center side frames of the two panels?

Thanks for the advise, bought the handles and screw/rivet nuts. Elected to use the screw head out on the visible door edge. Can see the rivet behind.