With the help of several folks who wrote in, I think I can identify the actors in the Bells Are Ringing clip who are dubbed by Paul Frees. Gil Lamb appears to be the one who opens the proceedings with the pratfall and some dialogue he speaks himself…then is later dubbed with a voice that sounds nothing like his by Inspector Fenwick. The one who sounds like Boris Badenov is probably Tommy Farrell, who was a prolific character actor in movies and TV shows, particularly playing sidekick roles in dozens of westerns and appearing in Kissin' Cousins with Elvis. I recognized him because he played Carl Reiner's agent in A Guide for the Married Man.
If that is indeed Tommy Farrell, there's a kind of "in" joke happening there, probably not intentionally. Throughout the song, Judy Holliday keeps mentioning Rin Tin Tin, because that's the only famous name she can think of at the moment. Well, Tommy Farrell had a recurring role on the Rin Tin Tin TV series. Another one of those silly things that only I would notice.