It's widely sourced that Fran Brill auditioned for the Muppets thinking she could just do voices, before Jim Henson informed her that the performers do the voices, which she did. But during the early years it was common for characters to be performed by non-performers, from having the human cast occasionally provide Anything Muppet voices (most notably Matt Robinson as Roosevelt Franklin, but it could be because Robinson created the character) to having various songwriters provide voices on occasion.
And Fran Brill's first Muppet production, The Great Santa Claus Switch, was also the first Henson production with involvement from Marilyn Sokol, who Jim quickly allowed to just do voices for the Muppets (if she continued to physically perform the puppets, I wonder if she'd still be a Muppet performer today). And following that special was The Frog Prince and The Muppet Musicians of Bremen, both of which used vocal talents from non-performers. Though GSCS was taped in New York while the other specials were done in Canada, and Jerry Nelson said in a Tough pigs interview that those required a certain number of canadian performers. Concerning TFP, Carl Banas was the only canadian voice actor in that special I know of, while Jerry Juhl provided the voice of Taminella (since he'd done the voice before and had stopped performing by then) and Jerry Nelson, who was a major Muppet performer by then, voiced but did not puppeteer Robin.