How can you convert a .zip file to a .exe file in linux?

Nope, as ZIP is an archive file

WINZIP can make a self extracting zip archive as an exe file. I don't know if there is an equivalent for Linux.

Linux dose not use or have the ability to run an .exe file. You can run many exe files in WINE, If it dose not run in WINE you can setup a virtual machine running Windows to run the program.