What time is it? Watches and horology

I have this Heuer Pasadena and would like to get a new strap for it. I'd like to fit a NATO, but it seems to be quite tight around the pins so I can't feed one through. I currently have a leather rally strap on it with a deployment clasp, but it doesn't feel comfortable so it means I'm not wearing it as much as I'd like.

try fitting the pins back on top of the nato.
so...take off the strap and remove the pins, place the nato where it should sit, then push back in the pins, I have done this with another lug covered watch.