I know of 3 Applications that use Java build in to the Application Bundle, Cyberduck, Vuze & Frostwire.
As i didn't get a reply yet, i went on doing some testing on my own. These are my conclusions.
Vuze: The easy one
It was very easy, open the App Bundle, look for the Java JRE which is in the Plugins folder, remove it. Now it uses the Java from the Internet Plugin installed by Oracle
Frostwire: The complex one
It wasn't working if i did the above, but at Oracle you can Download 2 versions of the JRE.
a DMG, which installs the Internet Plugin that comes with a Control Panel & Updates itself
or
a GZ, Which you need to install yourself in the Library/java/... or in my case in the Frostwire App Bundle Plugins folder, replacing the original JRE. This needs to be redone for each Java Update.
Cyberduck: The Unworking one
In the Cuberduck App Bundle the JRE wasn't in the Plugins folder but was in the MacOS folder were the Applications Executables are named Runtime.jre instead of JRE. However it's file/folder structure doesn't resemble the one of the earlier JRE folders. For example there is no binary folder. I couldn't find any other Java folders inside the Application bundle of Cyberduck.
replacing the Runtime.jre with the one from the GZ file from Oracle, of course naming it the same makes Cyberduck presenting an error.
Conclussion, Cyberduck Doesn't let you use the system installed Java or Update the Java inside the Bundle.
It would be nice that both Cyberduck & Frostwire use Java the same way as Vuze & that All 3 even add a small Application or script to remove Java from the Application Bundle if Java is Systemwide installed.