What, are you saying they made him a cockney when they showed it in the US?

Yes. One would assume that it might have had to do with negative Italian stereotypes, but it was the mid 80s (right?), and PC wasn't in full force back, so who knows?

Interestingly, I bought some Dangermouse on (commercial, legitimate) NTSC VHS (so intended for the US market) a long time ago that had his Italian accent, which is when I found out about this discrepancy.

What use is Stiletto without "Si, Barone"?

This was changed (IIRC) to ``Right, Baroney''. I always thought that was a slightly odd affectation (to put a trailing -ey suffix on Baron), but I just chalked it up to affectation, not lip (beak?) sync issues before I found out about the redub.

It sounded like that's the way it was originally recorded, so it wasn't a poor hack-and-slice audio edit. I have no real explanations, only evidence.