Mmm. My problem is that she's pausing in the middle of the sentence and that's how I'd experience it.
So if it was me, I'd say: "Certainly" and then I'd get stuck and realise I couldn't bring myself to say 'sir'. That'd be my experience and I wanted that to come over to the reader.
The example of explaining why she's about to pause before she starts to speak (which I think was Cul's??) was much more elegant, but I was going for staggering awkwardness rather than elegance because before she gets stuck, she doesn't know it's going to happen.
So if it was me, I'd say: "Certainly" and then I'd get stuck and realise I couldn't bring myself to say 'sir'. That'd be my experience and I wanted that to come over to the reader.
The example of explaining why she's about to pause before she starts to speak (which I think was Cul's??) was much more elegant, but I was going for staggering awkwardness rather than elegance because before she gets stuck, she doesn't know it's going to happen.