As long as you are not getting into trans sonic speeds or above, there will not be any significant change in your CP unless you have high cross winds. As I said, the effect of a cross wind is dependant on the speed it leaves the rail. If you take the sum of the velocity vectors of the vertical and cross wind speed, this gives you the effective angle of attack. RAS Aero will give you the change in CP based on the angle of attack.
@Chuck Rogers may be able to advise if RAS Aero will produce the correct base drag value for a stubby rocket. A 12:1 L/D ratio id not what I'd generally consider stubby.
Norm
As noted, a 12:1 L/D ratio is not considered stubby. The Base Drag model in RASAero II is applicable over a very wide range, and a 12:1 L/D is certainly within the range of a normal rocket.
Note that RASAero II does not include any stability effects of the Base Drag.
Take a look at the Angle of Attack from RASAero II or the other software packages, or you can calculate the Angle of Attack by hand. You can assume a Launch of Angle of zero degrees from vertical to simplify the calculation. With that Angle of Attack look at the forward shift in the CP in RASAero II. (Or RASAero II can do all this for you automatically, including the more complex angle of attack calculations when the launch rail is not directly vertical, but is some angle from vertical.)
A rule of thumb I like to use is that the Angle of Attack just off the Launch Rail should not exceed 12 deg. Most airfoils will go into a leveling off of Lift Coefficient (CL) at 12-15 deg Angle of Attack, and then the CL really falls off and the airfoil stalls. But it is pretty much a straight CL (and a straight CNalpha) with Angle of Attack up to 12-15 deg, with 12 deg the low (conservative) value to use as an Angle of Attack limit.
Note that the Fins can temporarily stall and Jet Damping (included in RASAero II) will keep the rocket pointy-end forward, or at least greatly slow the rotation of the rocket if it is unstable or marginally stable, and during that time period more propellant is being burned off and the CG moves forward. Again, all included in RASAero II.
I've proposed in the past an Angle of Attack limit when leaving the Launch Rail of 12 deg.
As others have noted, you can lower the angle of attack by flying in a lower wind, or by having a higher initial thrust to weight ratio to exit the Launch Rail with a higher velocity.
Charles E. (Chuck) Rogers
Rogers Aeroscience