probably things will get ugly
You are going to be taking about a fifth of the cross section off of that shaft, all off of the outside makes it have far more effect than drilling a hole and taking it off of the inside.
From 13mm to 11.65mm is likely to vastly change how the cue plays. Since you haven't mentioned current taper or taper you want to go to it is hard to even guess if this might work if you like how the shaft plays now. Just as an example, I liked how a shaft of mine played at 12.75mm. Same length, same pro taper, turning to 12.25mm totally changed the play of the shaft, made it unplayable for practical purposes.
If you like the play of the 13mm shaft I wouldn't cut it below 12.75mm. If that works you might be tempted to take a little more wood off. Just remember, expressed as a percentage, and in terms of playability, taking that first cut off of the shaft is a lot different than the last. Taking .25mm off may work from your viewpoint, another .25mm may make it unplayable. Even that first .25mm is a gamble. If you are really fond of the hit now I wouldn't cut the shaft at all.
Hu