It's my birthday, and as part of the days festivities I googled clarinetists playing "Happy Birthday." Here is Argentinian-born Israeli clarinetist, Giora Feidman. He is probably best known as the clarinet soloist for the soundtrack of Schindler's List to non-klezmer-fans, but he has recorded EXTENSIVELY. There is also the film Jewish Soul Music: The Art of Giora Feidman if you would like to know more about his playing.
We also have the "Ginasterical Happy Birthday" made by the students of Yehuda Gilad on his birthday.
And a personal favorite of mine - Wynton Marsalis Septet "Happy Birthday" with Victor Goines on clarinet.
Happy birthday to me, Gotthard Wagner, Madame De Pompadour, Charles Goodyear, Andrew Johnson, Etienne-Joseph Soubre, Carl Ludwig, Pablo Casals, Jean-Fernand Vaubourgoin, Willie Humphrey, Clyde McCoy, Robert C. Baker, Vitaly Alexeyevich Godzyatsky, Mary Tyler Moore, Jon Voight, and most of all Jude Law and LaToya London.