For the built-in TeX mode (i.e. not AucTeX), you can customize the variable tex-start-options: do C-h v tex-start-options and hit the Customize link. Enter --shell-escape as the value string, hit Apply or Apply and Save and try C-c C-c in your TeX file again.
EDIT: I see you said you tried this. I did too and it works fine. Maybe you didn't apply the customization? BTW, you can only tell by looking at the command at the top of the resulting *tex-shell* buffer: the prompt still says pdflatex (or whatever).