Whose 24-hour term as Senator is the shortest in the history of the U.S. Senate?

I think you might be referring to Rebecca Felton, but according to sources I can find she was in office for seven weeks, even if she was only in one sitting of the Senate for 1 day. Louis Wyman was in office for two days, and his is the shortest tenure period.

But while Felton only served in the Senate for a day, she was actually in office from Oct. 3 until Nov. 21-- seven weeks. Not the shortest tenure.

And that title might go to New Hampshire's Louis Wyman. As Alan Fox of East Lansing, Mich., reminds us, Wyman was the GOP candidate in the 1974 Senate race in New Hampshire for the seat being vacated by Republican Norris Cotton. That race, as many junkies might remember, was for the longest time too close to call. Cotton resigned the seat a few days early, on Dec. 31. Gov. Mel Thomson (R) then appointed Wyman to complete the term -- all two days of it (Jan. 1 and 2).

https://www.npr.org/sections/politicaljunkie/2009/02/whos_on_the_senate_short_list.html

Rebecca Ann Felton was chosen to replace Senator Thomas Watson who died in September 1922. One of the reasons she was chosen was that she was a prominent member of the Women's suffrage movement and the Georgia Governor, Thomas Hardwick (who was planning to run in the next general election) thought it was a nice idea that would earn him votes at the next election (but he lost...)
https://en.wikipedia.org/wiki/Rebecca_Latimer_Felton