Here is what ended up working:
,'your_query, for example, SELECT * FROM DB.SCHEMA.TABLE')
In addition to this query, part of the solution required me to add a registry DWORD value for the OraOLEDB.Oracle provider. That registry value was DisallowAdHocAccess with a value of '0'. Without this registry addition non-SA logins received an error:
Msg 7415, Level 16, State 1, Line 1
Ad hoc access to OLE DB provider 'OraOLEDB.Oracle' has been denied. You must access this provider through a linked server.
Once the registry was updated, everything works like a charm.