We study a quantum quench in the sinh-Gordon model starting from a large initial mass and zero initial interaction and quenching to any value of the mass and interaction. Such a quench can be approximated by a Dirichlet initial state which, being an example of a so-called "squeezed vacuum" state, can be evolved in time using earlier work . However the use of an idealized Dirichlet state leads to UV divergences and it turns out that the UV behaviour of the actual initial state is relevant to the calculation of physical observables. Based on a general method to expand the initial state on the post-quench energy eigenstates , we verify that the actual state is of the squeezed vacuum form and derive the correct UV modification that has to be applied on the Dirichlet state in order to describe a quantum quench. We compare with different UV regularization schemes that have been proposed and comment on the applicability of renormalization group tools in quantum-quench problems.  D. Fioretto, G. Mussardo, Quantum Quenches in Integrable Field Theories, New J.Phys.12 055015, 2010.  S. Sotiriadis, D. Fioretto, G. Mussardo, Zamolodchikov-Faddeev Algebra and Quantum Quenches in Integrable Field Theories, J. Stat. Mech. (2012) P02017, 2012.