What time is it? Watches and horology

Need a bit of advice / some ideas;

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.

That is lovely. Prefer existing strap. HTFU