I'm not talking an artificially-dyed Hollywood redhead, either. I'm looking for a word that perfectly recapitulates the kind of redhead who has lots of freckles, an extremely light complexion, and the kind of fiery red hair one would never mistake for the fake stuff. Basically, the stereotype of an Irish lass (though I've read that in fact the proportion of redheads among the English is higher).
Though not a single word, I've seen flame haired used for this and unlike ginger its very unlikely to cause offence.
As you mention though, the hair colour is not enough to identify.
Another phrase I've seen for this very purpose is Irish Rose which I'd guess grew from the more common usage of English Rose.