I'm sorry for your problems with the Copic odor. As far as I know, most markers similar to Copics are also alcohol based markers, and all will probably have an odor, some of them more than others. Prismacolor makes alcohol based markers, and I think they have more of an alcohol smell than Copics.
Bics and Sharpies also have an odor.
Here is a wonderful tutorial showing how to achieve similar results to Copics using the waterbased SU markers. I would think you could get a similar look with any waterbased markers, too, if you don't have the SU markers.
The waterbased markers should not have much odor, as they don't have an alcohol base.
No Copics No Problem - ON VIDEO!! - Paper Pleasing Ideas