I don't think Parkour should be a consideration AT ALL.
It's too modern, too specialized and is not in keeping with Cap's character at all.
Think about it, Steve Rogers is from the 1940s,(correct me if I have the dates wrong.) average guy, super strength, military training.
So his combat style would need to reflect the style and training of WWII US Military.
I wouldn't know details about that, but I'm thinking like, basic low level acrobatic, (not Spider-Man but more tumbling evasive manuevres) college wrestling style grapples and holds, maybe some boxing moves of that era, etc.
Overall I think Cap in the movie, when it comes to one on one, fist fight-- should be more brawn and brute force than anything overly technical.
In the Avengers movie, maybe he'll get an update, train with the new kids and modify his skill set.