Gravitational-wave observations of binary black hole (BH) mergers provide a novel avenue for testing massive-star evolution and the resulting BH mass spectrum. Recent population analyses under the hierarchical-merger hypothesis have provided evidence for the BH mass gap and inferred its lower edge to ∼44–68 M⊙. Motivated by these findings, we compute low-metallicity (Z = 10−5) helium star models with MESA and systematically explore the effect of uncertainties in the 12C(α, γ)16O and 16O+16O reaction rates on the final fate of these massive stars. Varying the 12C(α, γ)16O reaction rate from −3σ to +3σ, we find that the predicted BH mass gap shifts from ∼104–184 M⊙ to ∼45–135 M⊙. In contrast, scaling the 16O+16O reaction rate by global factors of 0.1, 1, and 10 has only a modest effect on the lower edge of the BH mass gap (less than 5 M⊙), and shifts the upper edge by more than 10 M⊙. Using the predictions of our models together with the literature estimates for the lower edge of the BH mass gap, we constrain the astrophysical S factor of 12C(α, γ)16O reaction at 300 keV of S300 ≃ 137.6–263.4 keV barn.