I just came across this because I wanted to hunt down where this rhyme came from.

Context: I've grown up in Pakistan and with a lot of exposure to a variety of cultures. I don't recall where I learnt this from as a kid, but the variation I know is as follows:

Salla walla wola
Walla walla wola
Clap clap clap, say
S- chico chico,
Chico chico chapstick,
Wallo wallo
Wallo
wallo wallo
Count - 1, 2, 3, 4

It's interesting to see the other versions. Also, we do not play this to the tune of ring around the roses.