After all these decades as an American, I can say I've never heard anybody anywhere pronounce it "Ry-o" outside of the song.

On the other hand....

Before the 20th century it was very common for English speakers to anglicize foreign pronunciations in ways that would be absolutely condemned today. (The way "Eye-rak" and "Eye-ran" are sneered at; there used to be "Jaypan" as well.)

"Ry-o" could well have developed among singers who'd read the name but didn't know Spanish - or didn't care.

Byron, for example, rhymes "Don Juan" with "true one."

So lighten up. Ree-o or Ry-o, BFD.

Finally, the practical requirements of chantey singing on shipboard have no bearing on the esthetic requirements of "chantey" singing on stage. In terms of repertoire, rhyme, rhythm, volume, and vigor, Hugill was a great chantey singer. But he needs no raves from me.