High thermal conductivity and the exorbitant cost of HH in half-Heuslers (HH) alloys limit the prospects for their applicability in thermoelectric (TE) energy conversion devices. However, by incorporating mass fluctuation and strain field effects in HH alloys, their TE performance can be optimized for which Hf has been used extensively. This work demonstrates the efficacy of a p-type acceptor dopant in (Zr/Ti)CoSb based HH alloys in enhancing the ZT by eliminating the use of Hf. A series of HH composition (Zr/Ti)CoSb1-x(Si/Sn)x (x =0 - 0.2) samples were synthesized by conventional arc melting and consolidated employing spark plasma sintering. Both Si and Sn doping were found to dominantly introduce hole carriers in the pristine (Zr/Ti)CoSb resulting in a p-type semiconducting. Optimization of carrier concentration by optimal substitution of acceptor dopants i.e. Si and Sn significantly improves the power factor and increases the phonon scattering resulting in an enhanced thermoelectric performance and a maximum ZT of 0.46 and 0.28 at 873K was obtained for optimally doped ZrCoSb0.8Sn0.2 and TiCoSb0.8Sn0.2 respectively. For further optimization, microstructural modifications by fine-tuning of the Ti to Zr ratio results in strain field effects and mass fluctuation in the optimised p-type (Zr/Ti)CoSb0.8Sn0.2 compositions which remarkably introduces additional phonon scattering resulting in maximum ZT of 0.8 at 873K for Zr0.5Ti0.5CoSb0.8Sn0.2. The present study provides a better understanding of p-type dopants in Half-Heusler materials by which prospective high thermoelectric performance can be obtained in low-cost Hf-free p-doped half-Heusler (Zr/Ti)CoSb alloys.