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Nuclear level densities (NLDs) and $\gamma$-ray strength functions($\gamma$SFs) have been extracted from particle-$\gamma$ coincidences of the$^{92}$Zr($p,p' \gamma$)$^{92}$Zr and $^{92}$Zr($p,d \gamma$)$^{91}$Zrreactions using the Oslo method. The new $^{91,92}$Zr $\gamma$SF data, combinedwith photonuclear cross sections, cover the whole energy range from $E_{\gamma}\approx 1.5$~MeV up to the giant dipole resonance at $E_{\gamma} \approx17$~MeV. The wide-range $\gamma$SF data display structures at $E_{\gamma}\approx 9.5$~MeV, compatible with a superposition of the spin-flip $M1$resonance and a pygmy $E1$ resonance. Furthermore, the $\gamma$SF shows aminimum at $E_{\gamma} \approx 2-3$~MeV and an increase at lower $\gamma$-rayenergies. The experimentally constrained NLDs and $\gamma$SFs are shown toreproduce known ($n, \gamma$) and Maxwellian-averaged cross sections for$^{91,92}$Zr using the {\sf TALYS} reaction code, thus serving as a benchmarkfor this indirect method of estimating ($n, \gamma$) cross sections for Zrisotopes.

Quasicontinuum $\gamma$-decay of $^{91,92}$Zr: benchmarking indirect ($n,\gamma$) cross section measurements for the $s$-process