As both a long-time developer and, more recently, a UI designer, I'd assert that having a UI designer for a 6 person user-base doesn't really make sense, unless

As both a long-time developer and, more recently, a UI designer, I'd assert that having a UI designer for a 6 person user-base doesn't really make sense, unless maybe it's 6 highly paid full-time users that are doing almost all of their work through it— in which case it would probably be critical. In my 20 year tech career, I've seen far fewer cases of "why was the UI designer so involved, here" than cases of "Oh, the developers will know what makes sense to users, so we'll just have a designer come in at the end and make it look nice." The latter is a much bigger mistake than the former.