Since Season 7 i have seen Armitage, Prometheus and Typhoons playing the DeWitt.
Although it adds variety to the mission, it is akward playing it as such, since stowiki also refers to the DeWitt as being a Typhoon Cruisers.. http://www.stowiki.org/U.S.S._DeWitt
Second issue is probably related to the first one, is that when u board it the DeWitt could be any of the 3 mentioned above, then when u finish with the captain, and depart to detroy it, it will have magically changed into another ship as well ....
Third issue with this mission is probably related to the location, when u interrogate the captain, u MUST use the boff-dialogue option to leave the ship, using the beam option next to the minimap will put you in sector space, unable to continue the mission.
Therefore u need to drop it, and select replay again, effectivly making u replay 2/3 of the mission.