As I have been known to sing both songs, I have previously noticed that the tune for the line "Call away the daighsoe" is a tad similar to that for "Cross the wide Missouri" in Shenandoah! But I sing them in slightly different keys - Bb for Sammy's Bar and C for Shenandoah.
It is perfectly possible that Cyril Tawney may have (unconsciously?) been influenced by it. But as its only six notes it could have been a coincidence and, anyway, what does it matter!
I agree with SandyJ, don't bother him now. But when he recovers fully it might be interesting to ask him.
"Don't mind the rain ...!"
Alan