I'm going to wake my wife up and get her to deal with the crying baby rather than doing it myself
Why can't you deal with the baby?
I have work to get done. I can't get distracted by the baby.
You and your wife both need to take responsibility for raising a child, and it is rude to skip your turn when she needs to rest.  However, if this is an unusual circumstance, and you really need to get your work done, it is okay to ask for help when you need it.  Just don't make a habit of waking your wife up when you could help the baby yourself.
I'm going to do what I want. If she is going to complain, I'm going to do it again.
You should not be acting that way towards your wife. You both need to help out the baby. If you can, you should calm the baby down before working instead of waking up your wife.