A search of music journals on JSTOR came up with
- "quarter note": 2,160 articles.
- "crotchet": 1,824
A brief survey of the articles suggested that "quarter note" is generally used by journals published in the United States, while "crotchet" is more used by journals published in Europe.
I'm an American English speaker and find the British terms confusing but not insurmountable. Over time, without any concerted effort, I'm learning them. Whichever set of terms you choose, a motivated reader will just look up the terms if necessary.
If you think your audience is likely to be unfamiliar with one set of terms or the other, you could include a brief legend at the beginning or end of the manuscript.
The entire question could be avoided by using the symbols themselves rather than words, if that's an option. For example, any reader of print who understands either "crotchet" or "quarter note" will also understand ♩.