I hadn't meant to dwell on the subject of who's been doing voices the longest for Disney but since I'm into it, let's carry the topic to completion. As many noted, my typing fingers transposed the date when Clarence "Ducky" Nash began playing a duck named Donald. It was 1934, not 1943, and I've corrected that.
Greg Ehrbar notes that Alan Young first did the voice of Scrooge McDuck (and apparently, Mickey Mouse as well) on the 1975 record album, Mickey's Christmas Carol. In 1983, that was adapted for animation and he reprised the Scrooge role. I don't know that he (or anyone) has performed as Uncle Scrooge lately but he's still the guy they'd call if they needed the character voiced so Alan inarguably is the currently-with-us actor who's been speaking for a notable Disney character the longest…
…unless you count Kathryn Beaumont. Chuck Wedge informs me that in recent years, she's been called upon to do the voices of Alice (from Alice in Wonderland) and Wendy (from Peter Pan) occasionally. Alice in Wonderland came out in 1951 and she recorded her part a few years before that. So she'd be the hands-down champ.
And leaving Disney aside, the person who's been doing a character voice the longest is, I suppose, Stan Freberg who, every once in a while, records lines for the diaper-clad Junior Bear in the Three Bears series for Warner Brothers. Stan first did the part in the 1948 cartoon, What's Brewin', Bruin? Can anyone think of anyone who predates Stan?