  By using the theoretical approaches describing well the available data on
$t$-integrated coherent photoproduction of light and heavy vector mesons in
Pb-Pb ultraperipheral collisions (UPCs) at the Large Hadron Collider (LHC) in
Run 1, we calculate the momentum transfer distributions for this process for
$\rho$ and $J/\psi$ vector mesons in the kinematics of Run 2 at the LHC. We
demonstrate that nuclear shadowing not only suppresses the absolute value of
the cross sections, but also shifts the momentum transfer distributions toward
smaller values of the momentum transfer $|t|$. This result can be interpreted
as a broadening in the impact parameter space of the effective nucleon density
in nuclei by 14\% in the case of $\rho$ and the nuclear gluon distribution by
$5-11$\% in the case of $J/\psi$.
