" Can I remove these from the lib folder for the exported exe without messing something up?"
Just try?

I don't know this exporter, so perhaps you can give some names of these extra jars? We can tell if they are from the JRE or from Processing.

Yeah I figured that would be necessary, just thought I'd see if anyone had any deeper knowledge on the subject.
By experimentation, it would appear that the only .jars that you need are:
core.jar
<myAppName>.jar
jsse.jar
sunjce_provider.jar
sunpkcs11.jar
ui.jar

and if using opengl:
jogl.jar
gluegen-rt.jar
opengl.jar
and their associated native files.

Caveat: only tested so far on my mac, and only tested to see if the game would start up and display its basic scene.
Interestingly, removing ui.jar during testing appeared to cause some kind of hang in the JVM itself, as putting the file back still wouldn't let the app start. Shortly after my firefox and even the console became unresponsive, and I had to reboot. Which for some reason reset the mac spotlight indexing. All this may be a one-time/unreproducible bug, but I'm none too keen to keep testing it. ><

The kind of files I was able to remove included:
apple_provider.jar
charsets.jar
classes.jar
j3dcore.jar
jai_core.jar
JavaRuntimeSupport.jar
jce.jar
localedata.jar
mlibwrapper_jai.jar

and several others.