  By adapting an ultraproduct technique of Junge and Zeng, we prove that radial
completely bounded multipliers on $q$-Gaussian algebras transfer to
$q$-Araki-Woods algebras. As a consequence, we establish the
$w^{\ast}$-complete metric approximation property for all $q$-Araki-Woods
algebras. We apply the latter result to show that the canonical ultraweakly
dense C$^\ast$-subalgebras of $q$-Araki-Woods algebras are always QWEP.
