If your security team want you to upgrade the JRE used by the DA agent, upgrade!! Starting with DA 6.3.2, the simple upgrade from the GUI will also upgrade the JRE used by the agent. All you need to do is fill out the right check-boxes. Both the agent and the JRE will be upgraded and the agent is brought back online at the end.
In prior releases you would have to insall or reinstall the agent software to have an option to also upgrade the JRE.