  In this article, we explore dynamical aspects of Out-of-Time-Order
correlators (OTOCs) for critical quenches, in which an initial non-trivial
state evolves with a CFT-Hamiltonian. At sufficiently large time, global
critical quenches exhibit a universal thermal-behaviour in terms of low-point
correlators. We demonstrate that, under such a quench, OTOCs demarcate chaotic
CFTs from integrable CFTs by exhibiting a characteristic exponential Lyapunov
growth for the former. Upon perturbatively introducing inhomogeneity to the
global quench, we further argue and demonstrate with an example that, such a
perturbation parameter can induce a parametrically large scrambling time, even
for a CFT with an order one central charge. This feature may be relevant in
designing measurement protocols for non-trivial OTOCs, in general. Both our
global and inhomogeneous quench results bode well for an upper bound on the
corresponding Lyapunov exponent, that may hold outside thermal equilibrium.
