The scotogenic model generates Majorana neutrino masses radiatively, with dark matter particles running in the loop. We explore the parameter space in which the relic density of fermionic dark matter is generated via a conversion-driven freeze-out mechanism. The necessity for small Yukawa couplings to initiate chemical decoupling for conversion processes naturally reproduces small neutrino masses as long as the active neutrinos are hierarchical. The model can also resolve the recently reported deviation in the $W$-boson mass while satisfying constraints from direct detection, charged lepton flavor violation as well as collider bounds. Parts of the parameter space lead to long-lived particle signatures to be probed at the LHC.