It does affect the hit significantly, but not sure how "soft" it will feel as I don't know the other elements of your cue..
That being said, a friend has a Nitti that was 13mm and he thought it was too stiff, and too hard so I suggested he take it down a little since he likes my cue's hit. He stopped at about 12.75 and thinks it plays much nicer..
I would recommend taking it down a little at a time and see where you like it.. Each tenth of a millimeter is a ton.. My main shaft is 12.4 and I have a couple backup shafts at 12.5 and I can tell the difference immediately in the spin and feel.