From Nato to Nato
Starting from the 12 o’clock end, pull the longer part of the Nato strap through the two spring bars, then through the floating keeper at the end of the shorter Nato strap. Pull the strap all the way through until it straightens.
From Nato to Leather
Pull the strap out through the floating keeper and the two spring bars.
Put the tool through the lug pinhole and press against the spring bar. Once the spring bar is released, remove it and set aside. Repeat on the other spring bar.
Slide the spring bars into the loops of the new leather straps.
Hold the dial firmly and insert one end of the spring bar into a lug pinhole first.
Once the first end of the spring bar is secure, use the tool to carefully compress the other end of the bar so you can slide it into the other pinhole. The spring bar should click into place. Repeat on the other strap.
Styling a watch appropriately for work need not be as complex as calculus with these three rules!