We study the dependence of the spin stiffness constant on the phosphorus concentration in the ferromagnetic semiconductor (Ga,Mn)(As,P) with the aim of determining whether alloying with phosphorus is detrimental, neutral or advantageous to increase the spin stiffness. Time resolved magneto-optical experiments are carried out in thin epilayers. Laser pulses excite two perpendicular standing spin wave modes which are exchange related. We show that the first mode is spatially uniform across the layer corresponding to a $k\approx$0 wavevector. From the two frequencies and k-vector spacings we obtain the spin stiffness constant for different phosphorus concentrations using weak surface pinning conditions. The mode assessment is checked by comparison with the spin stiffness obtained from domain pattern analysis for samples with out-of-plane magnetization and with ferromagnetic resonance experiments when more than one spin wave mode is observed. The spin stiffness is found to exhibit little variation with phosphorus concentration in contradiction with ab-initio predictions.