Apparently, there was a song recorded by the Cantrells called the Red Sombrero. I wonder if that's the song. I got the lyrics from one of "those" lyrics sites, but I verified the lyrics with the Cantrells recording - it's an exact transcription, and a very nice song..

THE RED SOMBRERO
(Mary Emily Cantrell, BMI)

Ever running to the sea
The way my dreams get away from me
The distant mountains stand so still
But the river is a wishing well
The river is a wishing well

Summer drew me to her shore
The river opened up her door
I stepped inside the cool retreat
To feel my mother's heartbeat
Just to feel my mother's heartbeat

Chorus:
I lost one shoe in the wild Missouri
But I don't care 'cause I'm in no hurry
Take it away downstream
Take my troubles, but leave my dreams
Take my troubles, but leave my dreams
Leave my dreams

Dreamers lose the light of day
But their nights are filled with golden clay
Hand me down a red sombrero
And let the river flow
Let the river flow

Chorus

I lost one shoe in the wild Missouri
But I don't care 'cause I'm in no hurry
Take it away downstream
Take my troubles, but leave my dreams
Leave my dreams
Leave my dreams


Source: http://www.lyricsdownload.com/cantrells-red-sombrero-lyrics.html

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There's also a very nice light classical/pops piece titled "The Red Sombrero." The Harry Fox Agency says it was composed by Lucien Calliet and Ronald Dinge. Mantovani recorded it in the late 1940s, but I don't know if that was the earliest recording.