(Known in the industry as the “Shat-Stammer.”)
I think that has something to do with a certain generation of actors who started out in Shakespearean theater. That was Shatner's training and, if you listen, you'll hear Charlton Heston do it, too (and not just in his "B" movies, but in the epics such as Ben Hur).
It’s way of saying:
“I’m a stone-faced actor who needs to convince you that my emotions are so deep I can hardly speak.”