Yes, you are right this is a mambo! It was originally a Spanish song written in Mexico in 1953 called "¿Quién será?" (Who will be (the one who wants me) etc.). It was translated into English by Norman Gimbel a year later for Dean Martin.
Here's the original Spanish version, sung by Nelson Pinedo:
By the way, if you don't know about this yet, the exhaustive Malcolm France site features a great jukebox, where you can choose all known songs from the series soundtrack!
All the people are so happy now, their heads are caving in.
I'm glad they are a snowman with protective rubber skin.
The latter also mentions a few yet to be identified songs but for the known songs the two seem to agree.
Yes, you're absolutely right about that. All of the identified songs come from Joe G.'s site you mentioned. Even Julie Glaze Houlihan herself, MITM's music supervisor, helped to identify a number of them on this site!
People can always mail him with other solutions, of course, if this still works (I know the site and its provider have had problems). This is just an image to avoid personal data harvesting: