Ignore the dog, don't correct. You're going to just teach him that interacting with your girlfriend is always unpleasant and that will be a huge problem later. Forget a prong and a shock collar, if he's energetic and being like that give him a short crate time out and then exercise him until he's tired, when he's napping do your work.
"he current issue we are having is that my girlfriend will be sitting in our office or on the couch at home working and he will approach her, mouth her feet/legs or mess with her in general and then when she pays attention to him, bark at her" - She should NOT pay attention to him when he does this, that's making him do it more.
" Mei vom Majic Forest