No no no, it's "itsy-bitsy spider"
Must be a regional difference. I've heard the "eency weency" version, but much more often it was "itsy-bitsy".
I wonder if you'll bump up against the fear of creepy-crawlies? If it's innate rather than learned, even the most cartoonishly cute bug might creep out a few kids. This'll be an interesting experiment; please let me know how it turns out.
