Actually they both are the same words with the same meaning. The spelling 'enquire' is used in British Isles and commonwealth. The equivalent elsewhere is 'inquire'.
Been chasing this one down (again) today without finding any authority for the usage you suggest. Tried a series of dictionaries right back to a 1911 Chambers in our in-house library. The dictionaries all equate the words, defining 'inquire' and simply referring to that entry against 'enquire'.
My vote is very much with the 'nice' (in the sense of 'worth preserving') distinction you ma