The reason I asked questions, is because everyone is different and different hospital seem to do things differently than others. So it helps to know what is going on. Some places try to have you up and sitting in a chair, if only for an hour at a time, the morning after surgery, working on your breathing excercises and start short walks just in the room. If so just standing and getting to and from the chair can make you a little SOB. Some other places/people even with out any complications, tend to relax the first day and mainly lay in bed or maybe sit up on the side of the bed and don't really start doing much until the 2nd day post op. So Being SOB, if he hasn't done much, would be even more of a concern, to me. Some people need the nasal O2 when they get off the vent the first day or so, others don't. Most of Justin's surgeries, he stays on a vent a little longer even while awake ( hour or so post op) But usually doesn't need/use O2 once it is out.
IF he is SOB but isn't using O2, he may need it. but I would ask questions until you are satisfied with the answers you are getting.