Is it possible to connect to Oracle using OS, or External, authentication, rather than specifying an explicit user ID and password?
Yes. You firstly need to enable External authentication both server-side, and also client-side (in your network configuration). Oracle cover this within Chapter 10 of their Advanced Security Administrator's Guide.
Having configured this -- and verified that it works correctly outside of your COBOL environment, for example, using Oracle's sqlplus utility, you can amend your SQL CONNECT statement to utilise OS authentication by specifying a username/password of / , i.e.