The website provided by George Seto (La Cucaracha and translation) should be bookmarked as one of the best sources of lyrics on the internet (Home Page: Folk Songs ).

In an early posting, Macca noted that the song was taken up by soldiers on both sides. The song crossed the border, and on both sides became the source of numerous parodies about every possible subject. In the 1920s and 1930s (depression era) the song was everywhere in the southwest, in English versions as well as Spanish.
In the "ingeb" site, the parody about "Preparation H" is an example of what may be called "border English" (not enough Spanish to be "spanglish."
Two verses from the American side that I remember from my high school days in New Mexico (about the girls of Albuquerque and Las Vegas- the one about Santa Fe girls is missing) are in the ingeb lyrics.

The women who followed the Villistas included wives, sweethearts and camp followers of more usual type. The women foraged and cooked for the soldiers. At the time, "cucaracha" was applied to the camp followers (some of whom fought alongside the men). They were the poor of rural Mexico.

Verse two at the ingeb.org site is one of the originals:
Pobre de la Cucaracha,
Se queja con deceptión,
De no usar ropa planchaza,
Por la escasez de carbón.
Poor is the Cucaracha, who complains disappointedly, she can't iron the clothes because there is no charcoal (for the irons).
Another:
Ya se van los Carrancistas,
Ya se van por el alambre,
Porque dicen los Villistas,
Que se están muriendo de hambre.

See the Carrancistas,
There they are in the stockade
Because, say the Villistas,
They are starving.
(Bitter reverse humor. Hope the translation is all right)