This paper presents an underwater acoustic channel simulation methodology that combines parametric modeling with stochastic replay of at-sea measured channel impulse responses. The motivation behind this approach is to extend the scope of use of replay-based methods by allowing some parameterization of the channel properties while complying with some level of realism. Such an approach is beneficial for extensive testing of communication links. The key idea is to deliberately distort the statistics of the experimental channel in order to meet some user-specified constraints. Our approach is based on a relative entropy minimization between the original time-varying channel impulse response and the simulated one. A particular attention is given to constraints on the channel Doppler spread and on the level of covariance between channel taps. The testing capabilities provided by parametric replay-based simulations are illustrated with real data collected in the bay of Brest, France.