A hybrid scheme, based on the high order nonlinear characteristicwise weighted essentially nonoscillatory (WENO) conservative finite difference scheme and the spectral-like linear compact finite difference scheme, has been developed for capturing shocks and strong gradients accurately and resolving fine scale structures efficiently for hyperbolic conservation laws. The key issue in any hybrid scheme is the design of an accurate, robust, and efficient high order shock detection algorithm which is capable of determining the smoothness of the solution at any given grid point and time. An improved iterative adaptive multiquadric radial basis function (IAMQ-RBF-Fast) method [W. S. Don, B. S. Wang, and Z. Gao, J. Sci. Comput, 75 (2018), pp. 1016--1039], which employed the $O(N^2)$ recursive Levinson--Durbin method and the Sherman--Morrison--Woodbury method for solving the perturbed Toeplitz matrix system, has been successfully developed as an efficient and accurate edge detector of the piecewise smooth function...