Word History: Why do we pronounce one (wŭn) and once (wŭns) while other words derived from one, like only, alone, and atone, are pronounced with a long o? Over time, stressed vowels commonly become diphthongs, as when Latin bona became buona in Italian and buena in Spanish. A similar diphthongization of one and once began in the late Middle Ages in the west of England and in Wales and is first recorded around 1400. The vowel sound underwent a series of changes, such that the word's pronunciation went from (ōn) to (ōōōn), with two syllables, to (wōn) to (wōōn) to (wŏŏn) and finally to (wŭn). In southwest England, this diphthongization happened to other words beginning with the long o sound, such as oats, pronounced there now as (wŭts). Only in one and once did this diphthongal pronunciation gain widespread usage.

I suppose there are several words that are similar to "one" in pronunciation.  However, we do not use them in the United States.