Is there a method to unzip .exe file on a Mac OS X without downloading and/or buying applications that do this for you?
The files cannot be "converted," but you can extract them; if the .exe was originally written in Java, this SO question should help. Basically, it explains that some Java to EXE packagers/compilers make them difficult to extract for various reasons.
Note that extracting the .jar files may or may not be legal, depending on the license included with the application.
JAR files are Java ARchives that contain a Java program's resources and class files, and EXE files are compiled executables. Already-compiled EXE files cannot be extracted of their original .jar files, but if they were only wrapped, you should check out JSmooth.
If you merely want to run the EXE file on your Air, WineBottler is an excellent Wine wrapper that allows you to run Windows EXE files, or you can install Windows on a virtual machine or using Boot Camp.