I think that the hyphenated variant 'no-one' is an outdated form rather than an example of a Br/Am difference.
You sometimes see it in older texts (early 20th century and before). It is fairly unusual nowadays, though.
The only advantage of the hyphen is to distinguish it from contexts where 'no one' has to be two separate words with the meaning of 'not one single [thing]' e.g. 'No one reference book will give you the full story: you will need to use several'.
I like Miriam's comment.
And also, sorry for being off-topic, Mr. Richard, just wanted to say that for some reason, I find it endearing how you always write both the American and the British spelling of a word using a slash ^-^
Su.Ki.... to the rescue
I was hoping you might respond.
I believe you when you say the hyphenated form may be antiquated but I would have thought that at least one dictionary would have cited it as antiquated, old-fashioned, obsolete, or archaic, but no.
Using the hyphen to distinguish between the pronoun and the term no one (meaning no single/individual thing) does make some sense, yet as I mentioned, I personally have never encountered it. Maybe I should read more than simple comic books :)