I'd figure an operator of his caliber can shoot ambidextrous. That's actually a relatively common skill for shooters ... I'm formally untrained, and I can shoot ambidextrous.
I have the Enterbay Bauer, so, if I'm going to buy a few bucks worth of 1/6 weapons, I might as well get stuff that'll work for either. If you're looking to identify movie weapons, IMFDB is the best site out there ...
https://www.imfdb.org/wiki/Main_Page
Bourne's pistols of choice were a Beretta 92, a Sig Sauer P225, a Glock 17, and a Sig Pro. The sniper rifle from the "you look tired, Pam" scene is some obscure thing, and may have been custom built for the movie. Good luck finding that thing. Bauer carried a Sig P228 and an HK USP Compact as his sidearms of choice ... but used virtually every freaking submachine gun and handgun ever built.
Not sure exactly what to buy. Bourne actually used suprisingly few weapons. The ones in Identity he usually picked up off someone and used briefly (if at all). There was the hunting side-by-side shotgun, though. Supremacy and Ultimatum had a few more, but still not too many.
SnakeDoc
