Of course a fitting would be the ideal place to answer your question.  That said I will share what I have found out.  The NS Pro 105T is the shaft Titileist expected to be used for the AP1...that says a lot.  Also, the AP1 head is heavier due to being oversized and if you decide to put in lets say DGS300 you will need to request the swingwieght to be adjusted (they can do that if requested) otherwise the heavier head and heavier shaft will move the swingwieght from D2 to D4...more than likely too heavy.  There are other light weight TT shafts and that also may be an option...quickly one can see a fitting with launch monitor is the only way to be sure...best regards.

Depends on what the club fitting data suggests!  Gotta be fit.

Nate, I agree with Ryan. No one swings the club exactly the same. This is why Titleist offers so many choices. Hope you go to your local Titleist Club fitter. -Chad