We know that whatsapp was not designed to send apk files that why it seems impossible to try such.
Without Dropbox or any third party apps you can send your favourite apps to your friends if you follow the steps below
HOW TO SEND APKFILES ON WHATSAPP
1. Frist locate the app you want to send
2. Get the apk of the app by searching it on your file manager if you didn't find it you need to backup the app NOTE apk format is like daniel.apk or anything as far as you've identified the app.
3. After successful backup go back to your file manager and search for the app again you will see the app.
4 Rename the app to daniel.txt
5 After that go to your whatsapp click on the share button then click on document
6 Now search for your app ie the one you saved in this format daniel.txt and send it
7 Now tell the person you sent it to that its should be renamed to daniel.apk
8 After that he can successfully install the app
Simple as ABC right?Let me see where you haven't got right through the comment box!