Abstract: It is quite conceivable that cosmology may give rise to appreciable populations of both particle dark matter and primordial black holes (PBH) with the combined mass density providing the observationally inferred value Ω_DM ≈ 0.26. However, previous studies have highlighted that scenarios with both particle dark matter and PBH are strongly excluded γ-ray limits assuming particle dark matter with a velocity independent thermal cross section (σv) ∼ 3 × 10⁻²⁶cm³/s, as is the case for classic WIMP dark matter. Here we extend these existing studies on s-wave annihilating particle dark matter to ascertain the limits from diffuse γ-rays on velocity dependent annihilations which are p-wave with (σv) ∝ v² or d-wave with (σv) ∝ v⁴. Furthermore, we highlight that even if the freeze-out process is p-wave it is relatively common for (loop/phase-space) suppressed s-wave processes to actually provide the leading contributions to the experimentally constrained γ-ray flux from the PBH halo.