I think the right word depends on what is going on for the speaker:
If they are naturally just not a fluent speaker, you'd probably say they are stammering, stuttering or faltering.
If they are nervous, you might say they are hesitating (or, again, faltering).
If they are being evasive, struggling to find words to avoid saying the wrong thing, you might say they are hemming and hawing, umming and ahhing or hesitating.
It's hard to neutrally describe a pattern of speech without imputing some kind of thought process.