Absolutely it's possible. There is no requirement to run ORDS with APEX, or even APEX with ORDS.
When you're asked about apex/apex public user, just say no or '2' to be specific.
Enter 1 if you want to use PL/SQL Gateway or 2 to skip this step :
Enter the PL/SQL Gateway database user name [APEX_PUBLIC_USER]:
Enter the database password for APEX_PUBLIC_USER:
Enter 1 to specify passwords for Application Express RESTful Services database users (APEX_LISTENER, APEX_REST_PUBLIC_USER) or 2 to skip this step :
Enter the database password for APEX_LISTENER:
Enter the database password for APEX_REST_PUBLIC_USER:
Enter 1 if you wish to start in standalone mode or 2 to exit :
Enter the APEX static resources location:d:\apex426\apex\images\
You can install ORDS with SQL Developer GUI wizard or you can do so at the command line, but the process is basically the same. There is an install and config guide here