My translation for the lyrics in the 1940 Mark of Zorro movie are:

It is possible, my Father,
That I shall come to suffer,
And that troubles shall come to pass,
By the fault of a woman.

Let my white hat be put on you,
Let my blue hat be put on you,
Let yourself sleep like a child in my arms,
Let me sing to you aru, aru, aru, aru (lullaby sounds in Spanish)

According to "The 1910 Trip of the H.M.M.B.A. to California and the Pacific Coast" (page 211) on Google Books, the song was sung as men and women danced. Acceptance to wear the man's hat by the lady signified acceptance of his suit. The lyrics in this book are somewhat different from those in the Mark of Zorro.