Guest Number Two Squillion: First of all, the proper title of the song is "I Hold Your Hand in Mine" (not "I'll"). And as to the matter of the tune...

On this page, you'll find a Tom Lehrer CD and, if you scroll down to the song list, you'll find links to a clip of a portion of the song (for Music Sampler and Windows Media). Fortunately it's a recording of the middle of the song, which is the trickiest part.

Click on the "Download MP3" link on this page to hear a choir sing the entire song. They changed one word, though: they sing "little bite", which should be "healthy bite."

Mick Pearce has posted a good set of chords so, between that and listening to the tune, you should be all set.