You're right. Though https://en.wikipedia.org/wiki/Boatswain says "formerly and dialectally also /ˈboʊtsweɪn/ BOHT-swayn", the dictionaries I checked do not list that alternative.

https://www.etymonline.com/word/boatswain even comments:

> Phonetic spelling bo'sun/bosun is attested from 1840. Fowler [1926] writes, "The nautical pronunciation (bō'sn) has become so general that to avoid it is more affected than to use it."