I've just fixed the broken gun to get the M19, but I can't seem to equip it?
If I stow the original pistol away, I just get nothing for slot 2?
To equip it go into your inventory and move into one of the top slots. R is default control on keyboard (and X if you are using XBOX controller) to select it and then move with arrow keys.
You can have both pistols equipped and assigned to different buttons.
See game guide