Just set the classpath when you execute the java command...

#!/usr/bin/perl
# perl stuff here

`java -classpath /cygdrive/c/java/myclasspath myjavathingy.class`

# more perl stuff here
[download]

Also Cygwin in my experience usually doesn't change Windoz variables so you should be safe if you want to set the classpath variable when you open up Cygwin.