As a developer of ctex package, I'd say: ctex does NOT support latex+dvips approach by default. And zhmetrics does not provide mapping files for ttf2pk to create PK fonts on the fly.
When compiling with latex command, ctex package uses zhmetrics with default zhmap option. Then zhwinfonts.tex is used and TrueType font mappings are configured for dvipdfmx only. And when compiling with pdflatex command, TureType font mappings are configured for pdfTeX. Dvips do not support this, and we do not support dvips.
You can only use one of these to compile your documents:
latex + dvipdfmx
pdflatex
xelatex
If you insist on dvips, you must use ttf2pt1 or fontforge to convert the TrueType fonts to type 1 format. Then write a font mapping file and use updmap utility to install them.
Or, you can write proper ttfonts.map to get bitmap fonts on the fly.
After that, you can use ctexart with nozhmap option to use type 1 or PK fonts. (It is illegal as I know.)
Type 1 Chinese fonts are only useful for MetaPost. It is not recommended to use type 1 fonts.