  QCD sum-rules are used to calculate the $\hat\rho(1^{-+})\to\pi\eta,
\pi\eta'$ decay widths of the exotic hybrid in two different $\eta-\eta'$
mixing schemes.
  In the conventional flavour octet-singlet mixing scheme, the decay widths are
both found to be small, while in the recently-proposed quark mixing scheme, the
decay width $\Gamma_{\hat\rho\to\eta\pi}\approx 250 MeV$ is large compared with
the decay width $\Gamma_{\hat\rho\to\eta^\prime\pi}\approx 20 MeV$. These
results provide some insight into $\eta$-$\eta'$ mixing and hybrid decay
features.
