I am not familiar with your models and their caveats, so I cannot speculate how your effective field theory imagines this vertex, $ie'A'_\mu\bar \chi \gamma^\mu \psi $ + c.c., exists for massless vectors which are not gauge bosons. The model should be non-renormalizable, but model-builders are pretty unscrupulous these days...
The Feynman diagram you have is meaningless Feynman-diagram-junk, as common in experimental talks with a Feynman-diagram fetish, in that it suborns the viewer into assuming it represents a term in an existing legitimate theory, of the "you-know, you-know" type.
Let me stress again what you must already know, namely that a massless gauge field $A'_\mu$ is completely out of the question, because it should couple to a conserved current, and your $\bar \chi \gamma^\mu \psi $ cannot be conserved unless χ and ψ have the same mass, so the fermions have a global U(1) symmetry before the introduction of such gauge fields.
I have little experience with non-gauge vector fields, against which the whole world of Lorentz consistency is arrayed, but that is a very different question I would not touch.