The decay of the 13/2$^+$ isomeric state in $^{183}$Hg was observed for the first time following the $\alpha$ decay of the 13/2$^+$ isomer in $^{187}$Pb produced in the $^{142}$Nd($^{50}$Cr, 2p3n) reaction. Using $\alpha - \gamma$ delayed coincidence measurements, the half-life of this isomer was measured to be 290(30) μs. This isomer is proposed to deexcite by an unobserved low-energy M2 transition to the known $9/2^-$ member of a strongly prolate-deformed $7/2^-[514]$ band, followed by a 105-keV M1 transition to the bandhead. A lower limit of $B(M2) ≥ 0.018$ W.u. was deduced for the unobserved transition. The presumed retardation is proposed to be due to the notable shape change between the initial, nearly spherical, and the final, strongly deformed, states. A similar scenario is also considered for the 13/2$^+$ isomer in $^{181}$Hg, suggesting both are cases of shape isomers. The B(M2) systematics of neutron transitions across the nuclear chart is discussed.