According to this OpenJDK bug report (https://bugs.openjdk.java.net/browse/JDK-8023821) there are three possible workarounds:
Sign the jnlp file. Use either a signed-jnlp file (JNLP-INF/APPLICATION.JNLP) or a signed jnlp template (JNLP-INF/APPLICATION_TEMPLATE.JNLP).
Use secure properties. Change all the properties in the jnlp file to pre-pend "jnlp." to the property name, and modify all code to use the new properties name.
Use secure properties and translate them in the main of your signed application to insecure properties. Change jnlp files to have the property names in the jnlp file pre-pended with "jnlp.myapp.", then in your application read the system properties and for each property starting with "jnlp.myapp." set the corresponding property without the "jnlp.myapp." pre-pended to the name.
It sounds like 2 and 3 are not what you want. So that leaves you with option 1. (Or accept that you need to change your codebase.)