Is the airspeed for the minimum the same for the theoretical power required curve as for the shaft power required curve?
The OP is asking about power required, not power available, which, in my mind, would change the answer.

From an aircraft performance perspective, power required is the product of total aircraft drag and inertial speed ($P_R=TV$), applicable only for steady unaccelerated flight. Thus, the minimum of that curve is dependent on profile and vortex drag. In potential flow, it would be where $3C_{D_0}=C_{D_i}$ (see this answer for derivation).

Shaft power required is the power needed to be transferred to the propeller in order to achieve the aforementioned $P_R$. From the actuator disk theory, we know that it must be larger than $P_R$. The shape of this curve would depend also on the propeller itself (e.g. pitch, diameter, airfoil) and its control system (e.g. constant vs variable pitch). Therefore, the minima of the two curves do not have to coincide.

To illustrate this, I've gathered some RC propeller data from APC, which according to its website are generated based on vortex (potential) theory. The drag polar is based on a joke planform designed to accentuate the curvature of the polars:


$C_{D_0}=0.02$ (this is way too low for an RC planform)
$e=0.85$
$W=25lb$
$A=8$
$S_{ref}=15ft^2$


The figure below shows the power required (P_R) for level flight and the shaft power (torque * rotation speed) needed to sustain the level flight for a few prop configurations.