The version I grew up with in the 90's was:

(you stand in a circle with one hand on top of the others and slap the next persons hand as it goes around the circle while you sing)

Down by the banks of the Hanky Panky
Where the Bullfrogs jumped from bank to banky
With the eips ipes opes skiddle scaddle ding dong

we would sing that to pick the person who would stand in the middle for another rhyme:

I was going to Kentucky
The old Kentucky fair
When i met a seniorita with purple underwear
OH shake it to the bottom(go down)
Shake it to the top(come back up)
Spin around, spin around(spin around with eyes closed)
Till you S-T-O-P spells stop

The person you were pointing at would be the next person to start and we would sart all over again.