I have to do a little "name-dropping" here, I can't resist.
Much of the karate done in "Walker" was done by his stunt-double, one of his first students, named Chip Wright. He looks just like him, and is an 8th degree black belt under Chuck Norris. It's a good chance that he's the one you're seeing in the shots where it doesn't show Mr. Norris' face directly.
Mr Wright is my instructor.
At my school we say that the reason Chuck Norris is so quick is that there are actually two of him.