When Rachel Maddow takes a vacation or is out sick from The Rachel Maddow Show, Alison Stewart usually fills in as guest host. I don't know if it's a case of not enough prep time or just not being very good at reading the teleprompter, but she seems to have a lot of trouble getting her words out.
She trips over her tongue about once per paragraph, her stumble sometimes only slightly noticeable ("ot" for "not") and sometimes unmistakable ("If your conspiracy theater...theory...spidey sense is going off right now...").
On last night's show she acknowledged her awkwardness mid-sentence:
"But you won't spit your lime thirky lick...(laughs) oh, boy. You won't spit your lime rickey through your nose in surprise...."
News readers and talk show hosts will not usually acknowledge a mistake; there's just no time to keep backing up and saying, "Excuse me..." in the middle of a sentence. They just keep plowing through their script, hoping for the best.
We all make these little stumbles from time to time, and inexperienced speakers who are trying to be perfect can find them embarrassing and feel a need to acknowledge or apologize.
Let me suggest that you follow the news readers' cue and let these stumbles just roll on by. If you ignore them, the audience will, too. In the case of Alison Stewart, it's hard to ignore as it's a regular occurrence. But for most of us, who aren't filling in at the last minute for a talk show host and reading from a teleprompter, it shouldn't be that much of a problem.
In the case of a "lime thirky licky rickey" type of moment, I think a little humor is called for. I have tripped over my tongue like this in presentations, and it's pretty funny. So go with it. Have a laugh, say "oops" and move on.
As with most minor mistakes, we're all human and your audience appreciates that about you!