We played this "French skipping" in Southport, Lancs in the late 60s. I was under the impression my mum (b.1940) knew it - she certainly did it with us and contributed some rhymes (but maybe they were from her two/three balls repertoire).
As per Sophie's comment, I does indeed look as though some of the 'nonsense' rhymes are corruptions of Japanese - counting from one to ten in Japanese:Ichi, ni (nee), san, shi, go, roku (loku), shichi (hichi), hachi (youtsu), ku, ju, matches "Itchy, me, star, shee, Lo*, go*, hutsy, yutsy, kill, it" (*these two have switched position) and "Hootchie Kootchie" (8-9-10, which could be interpreted as the 8th and 9th place in the rhyme "Eeny meeny pepsi seeny, Ala-bama, boo! Hoochie kootchie, donna loochie, OUT GOES YOU!".
Also "Yoka ana Tysa, Yoka ninety-ay, Tang in de soeboy, Sooey sooey ay" sounds like Japanese: Yoko = side, ana = hole (middle?), soba e = to the side, sore sore-e = yeehaw!