I'd do this: have an honest talk with your wife about why she thinks they'd be offended. Because honestly, this fear is usually blown out of proportion - people understand that weddings are for close ones, and that's totally normal.
If your wife says some specific coworker would actually be hurt, then that person is more than just an office acquaintance to both of you. In that case, it makes sense to invite them. As for the rest, you can skip the invitations - just mention in conversation that the wedding is by invitation only, family-style format. People respect that.
I've seen a few situations like this - the ones who tried to invite everyone from their work contacts ended up regretting it: the celebration turned into this huge, expensive thing that felt impersonal. When they invited only close people - everyone was thrilled and felt the real atmosphere.