You can tell SQL Developer to use a 'thick' connection which basically pulls in your full Oracle client. Have you tried that?
We have setup SQLNet FIPS140-2 encryption that works fine with the full Oracle SQLNet client. But using SqlDeveloper via a JDBC thin connection, it is unclear how to enable to work with the FIPS 140-2 connection.
Only someone from the Sql Developer team can tell you what their product is capable.of.
You can certainly configure the JDBC thin client to support the equivalent of what the thick client does but whether sql developer provides any means to supply the necessary info only the team can tell you.
I suggest that you first create a sample JDBC test app that uses the settings you plan to use and then edit your question to provide the specifics to see if they are supported.
See Chapter 14 'Configuring the Thin JDBC Client Network':
This chapter describes the thin JDBC client implementation of Oracle Database network encryption and strong authentication, which lets thin Java Database Connectivity (JDBC) clients securely connect to Oracle databases.
The Java implementation of Oracle Database network encryption and strong authentication provides network authentication, encryption and integrity protection for Thin JDBC clients communicating with Oracle Databases that have Oracle Database network encryption and strong authentication configured.
As that doc section also says, see the JDBC Developer Guide, for further info.
For JDBC there is no SQLNET.ORA file and that is where settings for the OCI client would be specified. Instead you specify properties for the DataSource used for the connection. I have no idea how the sql developer client connects internally, whether or not they use datasources as part of the connection and, if they do, whether they have, or plan to have, any way (GUI window or properties file) for the user to set the appropriate datasource properties.