Nonadiabatic transitions in one-dimensional charge-density-wave models are investigated. In these models, the twofold degeneracy of the ground state, which usually exists in a half-filled electron-band case, is lifted to yield stable and metastable ground states. In this article, we particularly treat the case where a system in the former state is photoexcited. Since our model has no Coulombic interaction between electrons, a photoexcited state is expected to relax down directly to a bound soliton-antisoliton pair. However, this relaxed state itself has a finite lifetime because of various decay channels. Here, we focus on nonradiative decay channels and try a semiquantitative method that restricts the modes of phonons, to clarify expected features of nonadiabatic transitions in these systems. The selected modes are not only the relative coordinate of the two solitons, but many long-wave modes. Closely examining each contribution, we find for the first time that the latter modes essentially enhance the transition probability, which result is deeply related to valence-conduction hybridization in the electronic midgap states. The obtained values are comparable, at least in the orders of magnitude, to the experimentally measured lifetimes of self-trapped excitons in halogen-bridged mixed-valent platinum compounds. Moreover, we also confirm that the same probability becomes larger with a reduction of the degree of nondegeneracy, which result is consistent with the concept of a soliton pair as a relaxation path from photoexcited states.