I'm not 100% certain all of these were recorded in the US, but I think most were. They were all released on US labels. As reference Atlantic and Capitol released singles by Prince Buster and Byron Lee respectively in May 1964. The craze seems to start in early May 1964, with ska getting mentioned in every issue of Billboard from May through August, though the full featured stories are mostly in the May and June issues, with later mentions only being in passing reference to record releases. After August ska only get a rare passing mention every couple months. It appears it was strictly a summer craze.
Jerry Kennedy "Blue Beat" May 1964. From Billboard, May 16, 1964: “Because of the strong reaction here to the Millie Small disk, Smash last week rushed Jerry Kennedy, its Nashville a&r specialist, into the studio for a Blue Beat instrumental. Fetch says a Blue Beat dance craze is on the way and he intends to be in on it from the start”
Toni Fisher "The Train Of Love" June 1964. (I don't know that I would have picked this out as ska, but it seems to have been marketed as such on release).
Ray Rivera "Do The Bluebeat (Jamaica Ska) June 1964.
Al Garcia & The Rhythm Kings "Latin Ska" June 1964.
Mark Thatcher "The Bluebeat (Jamaica Ska) June 1964.
Tracey Day "Ska-Doo-De-Yah" June 1964.
Baby Earl & The Trini-Dads "Everybody Do The Ska" June 1964.
Woody Herman released "Come On And Ska" July 1964.
Mr. Acker Bilk & His Paramount Jazz Band "Dream Ska/Ska Face" July 1964.* Upon further research, this is a UK recording
The Fleetwoods "Ska Light, Ska Bright" July 1964.
Mango Jones & His Orchestra "Coffee Street Ska/Ska La Bomba" July 1964. *This may be a Jamaican recording?
The Pussycats "Come On And Ska" July 1964.
The Cambridge Strings "Charmaine - Ska" July 1964. *UK maybe?
H.B. Barnum "Ska Drums/Skakiaan (Skokiaan)" July 1964.
Frederick Fennell & The Fennell Symphonic Winds "Seventy Six Trombones Ska" - July 1964. Okay, I have to point this one out, and request that anyone who has this to please upload this to youtube. It sounds like it must be amazingly terrible. From the July 25th, 1964 Billboard Magazine: "Mercury Records’ classical division last week shipped its first single - in the ska trend. It features Frederick Fennell and his Symphonic Winds playing “Seventy Six Trombones Ska”
Claus Ogerman & His Orchestra "Summer Ska" August 1964.
Jimmy Griffin "Try" August 1964.
Toni Wine "A Boy Like You" August 1964.
Lester Lanin "West Indies Ska" August 1964.
Rockin' Rebels "Bongo Blue Beat" August 1964.
Bobby Jay & The Hawks "Everybody's Doing It #2 - The Ska" LP August 1964. (I've always wondered about the #2 on this album, it turns out that they released 3 albums of different current dance crazes, The Watusi, The Monkey and The Ska.)
Baja Marimba Band "Baja Ska" September 1964.
Dean Jones "Women (Ska-Da-La-De-Da)" September 1964.
Lloyd Thaxton "The Tennessee Ska" October 1964.
The Mark III "Let's Ska At The Ski Lodge" October 1964. Featuring a young Grover Washington on sax!
Roscoe Weathers "Lost And Lonesome Ska" December 1964.
Throughout the stories Billboard first identifies Cleveland and Detroit (!?) as the centers of the ska craze, then later in the summer an Atlantic rep points to Philadelphia and the Jersey Shore as the hottest markets for ska.
*edit to add more 1964 records where I can't find the month of release
Ray Barretto "Ska Cha"
Al Russ & His Orchestra "Ska-Cha-Cha"* Actually a 1956 release and unrelated
Jack Hansen & His Orchestra "Calypso Ska"
Unnamed Crown Studio Band "Texas Ska" (from Crown 5449 Discotheque LP)
The Hip City Five "Jamaica Ska"
Milton DeLugg & Orchestra "Three Blind Moose (Blue Beat Ska)"
The Bon-Aires "Blue Beat" (There are several references online to this being a 1963 (or even 1962!) release, I simply don't believe that could be though).
Connie Dee "My Boy Lollipop"
Teresa Brewer "My Boy Lollipop"
Marty Gold & His Orchestra "My Boy Lollipop"
Stave Alaimo "Everybody Likes To Do The Ska"