Regularization of Mickelsson generators for nonexceptional quantum groups

Let $\mathfrak{g}'\subset\mathfrak{g}$ be a pair of Lie algebras of either symplectic or orthogonal infinitesimal endomorphisms of the complex vector spaces $\mathbb C^{N-2}\subset\mathbb C^N$ and $U_q(\mathfrak{g}')\subset U_q(\mathfrak{g})$ be a pair of quantum groups with a triangular decomposition $U_q(\mathfrak{g})=U_q(\mathfrak{g}_-)U_q(\mathfrak{g}_+) U_q(\mathfrak{h})$. Let $Z_q(\mathfrak{g},\mathfrak{g}')$ be the corresponding step algebra. We assume that its generators are rational trigonometric functions $\mathfrak{h}^*\to U_q(\mathfrak{g}_\pm)$. We describe their regularization such that the resulting generators do not vanish for any choice of the weight.