I'm sure the wedge pin/wedge pin pressure has a lot to do with your accuracy issue. I have a small engraver and all my wedges are marked with a "T" to indicate which side goes on top.
And if you mean by tapping - a light tapping as with a pocket knife or similar light object and not with a mallet then that is about the pressure most of my sidelock wedges need too. I only have one where all that is required is firm thumb pressure and it sort of snaps into place.
I use one of those combo wedge hammer/wedge puller/nipple wrench tool from T/C. A handy little gadget that I think you can pick up at Wal-mart.