Functionality has been added in Spectrum version 10.2.2 to allow the java configuration for 32bit/64bit clients to work. First you will need to upgrade to Spectrum 10.2.2 or greater. Then you need to configure the <resources> tag in the $SPECROOT/tomcat/webapps/spectrum/oneclick.jnlp file as noted in the file:
<!-- If you wish to force 64bit or 32bit OC client, replace <resources> tag with one that
specifies an architecture - "amd64" for x64 and "x86" for x32, see below examples.
You can copy oneclick.jnlp to oneclick32.jnlp or oneclick64.jnlp, and customize platform & memory,
and then new launch points will be added automatically to OC admin page.
Note: For arch specifiers to work properly, you must exactly match the JRE version or
make sure the "Allow new versions" checkbox is checked in the supported
JRE Version configuration.