Can You use the word “kerfuffle”in formal writing? YES. Vocabulary.com
A kerfuffle is some kind of commotion, controversy, or fuss.
You tell your little girl everything will be okay, or you tell your
tween how to handle a friend kerfuffle, or you commiserate with your
teen who’s complaining that his teacher hates him. Washington Post
Aug 21, 2019
And from WorldWideWords:
Though the White House spokesman Ari Fleischer used it in January
2002, it hasn’t been especially well-known there and a later
presidential usage caused something of a kerfuffle:
President Bush used “kerfuffle” Monday during an appearance in Ohio,
and in so doing, he created a minor one himself. Some of the
president-watchers on duty in the press gallery had to stop in
mid-story and explain to America this novel new word from the man who
gave us “misunderestimated.” The Lima News (Ohio), 22 Mar. 2006.
Listed as informal in BrE, In AmE it is not always so designated. AmE is also 'looser' than proper BrE, for better or worse. My sense is it can be used formally or informally, at least in AmE. Now 'bloody hell' ... that's another kerfuffle, and it not over the use of hell.