A shoulder rig is really not made to go
under a dress shirt or typical button-downs. Too bulky. There are a couple of under shirt options, but I blank on the names. Look for Threads started by "Fed_wif_a_Sig". Other members will add options too.
My wife uses a Sam Andrews "Monarch" with light weight over-blouses a lot tho.
Belly-bands are an option too. Smart Carry also?
Look for Fed_wif_a_Sig's post (one of several) here. He knows exactly what he talks about. The real deal.
undershirt holster
Here's another:
http://www.smartcarry.com/
BTW, welcome.