How to set the Tektronix oscilloscope for pre-triggering?
The first few videos in this playlist may come in handy:
https://www.youtube.com/playlist?list=PLzHyxysSubUkc5nurngzgkd2ZxJsHdJAb 

Basically, you'll want to trigger on the first channel and use cursors to measure the time delay between the switches.

First, put the scope into "normal" acquisition instead of "auto" acquisition mode. Then, set your trigger threshold somewhere between the max and min of your signal (rising/falling edge trigger will be fine). Then, set your time/div setting to have at least 200 usec on screen. Finally, hit the "single" button and wait for your switch to change.