That's a very nice watch to remember your father by
Re. Omega straps - if I was you, I'd completely avoid modern Omega straps as they are too thick. The padded design is a good fit on modern, beefier watches, but not so much on the slimmer models of the 60's.
If you find an original strap, chances are that the leather has become fairly brittle or that it will wear out fast. Add to that the fact that original Omega straps are quite pricy for what they are, I'd look for a non-padded aftermarket strap and perhaps add an Omega buckle to it. You'll want a strap that is 18mm at the wide end and 16mm at the slim end where the buckle sits. Beware of counterfeit buckles - it will look something like this:
https://omegaforums.net/threads/about-omega-buckles.37347/
Here are som NOS straps (same source as above) :
Click to expand...