Skye Boat Song Setting

I have just become the music editor for a band and have been challenged on my setting for 'Skye Boat Song' - not for an embellishment, but for a melody note. Looking online, I see that both versions are common.

In the second part, second bar, the first three notes (𝅘𝅥𝅮.𝅘𝅥𝅯𝅘𝅥𝅮) are either:

• E C E (mine)
• E B E (band's)

Based on nearly all other instrumental sheet music I found, the second one is correct. But the first also seems equally common in bagpipe sheet music.

I will make the change, but I am curious about the history of the alternative and am wondering if anyone has any ideas about how it became common.