If you wash the vape after what? The other person uses it?
Depending on when the vape is washed, maybe. If you are faithful in cleaning it between someone else using it, and you using it, then no. If not, then yes.
This would be like sharing drinks, utensils, etc. Make sure to use something totally disinfecting - soap, alcohol - whatever is safe for the vape.
Oh and this is only for hsv1 orally. You can't get genital herpes type 2 from any oral exposure.
It's also still cold and flu season in many places, so maybe just don't share things.