The main reasons that the UK and Commonwealth areas landed on "SH", as I see it:

-Musicologist RR Terry proposed the then most-common "CH" spelling be changed to "SH", to "reflect" pronunciation. Now, whenever English spelling has consistently "reflected" pronunciation in recent centuries, please tell me. I seem to get on fine by learning pronunciation of words before or as I learn to spell them. Anyway, Terry made that proposition at a meeting of the Royal Music Society in 1915, and it was dismissed by colleagues. The British authors of chanty collections up to that point had been using "CH."

-However, in 1921, Terry went on to publish a VERY influential collection of songs in which he used his rationalized 'SH" spelling. The 1920s saw a boom in popularity of these songs, several being commercially recorded, and a glut of more collections followed.

-Colcord (American), for one (there were others) consulted Terry's work closely when preparing her own in 1924. She decided she'd like to use "SH". Her work was also widely consulted, and these 1920s works began to replace things like Davis & Tozer's (1887, British - CH), LA Smith (1888, British - CH), Whall (1910, British, - CH), and they were more available or useful for performers than study works like Bullen (1914, British - CH) and Sharp (1914, British - CH) and other British folklorists of the early 20th century.

-Thus in the 1920s, SH became well established (though not dominant).

-Hugill (1961), following in this trajectory, used SH, and his work became a standard reference work. Following, many have chosen to use SH for the practical reason of being "consonant" with Hugill's well known work. I had to read a paper on the subject in England, and I made sure to use "SH" so as not to cause any unwanted "dissonance" with what I knew to be the local preference. I wanted my ideas to be heard, and didn't want the spelling to be a distraction.

-Concurrently: Though not the earliest, one of the earliest published spellings, in 1869, was SH. Oxford English Dictionary picked up on this as their "earliest" appearance of the word, and it has been enshrined as such, though CH spellings were a lot more common in 19th century writing on the subject.

-If I may be permitted a snide remark (I believe this is OK on Mudcat): British people (ugly generaliSation here - deal with it!) tend to take the position that what they do and how they do it is by default the proper thing...and so they have rested, for some many decades now, confident and comfortable with the rightness of SH. Americans (bias generaliZation alert) tend to be more open in their attitude. CH, having been historically extablished already, continued to be used by researchers like RW Gordon, JM Carpenter, and Alan Lomax, and used by influential purveyors of info like Mystic Seaport. And as such, CH doesn't appear as dissonant to the eye.

-Generalizations aside, each person has his/her own reasons for using whatever spelling, which may be independent the way the spelling developed in nations post-1920s. But my point has been to explain the situation *generally*.