Firstly, if the apk is not handy and needs to extracted from the installed app, use the Apk Extractor to extract it and save it to your device.
Browse to the file that you want to share and edit the file extention. In simple terms a file extention are the last letters that you see after the file name. For example the whatsapp file has a file extension of APK so in your File Manager you should be able to see something like this, whatsapp.apk
Nowusing your File Manager convert the file that you want to share to a document format by editing the file extension. For example whatsapp.apk should be converted to whatsapp.doc simply by editing the file extension.
That's it, now save the file in any location on your device and share it on WhatsApp Messenger as a document.
NOTE: Whoever receives the document must also convert it back to an APK file in order to install it on their device. This trick also works for files with file extentions like zip, rar, exe, jar, pdf to mention but a few. Softek Systems™ Enjoy!