This is not really an AI2 question…
You need to decide what is the best online host for your app, if you are not going to use Google Play or any other App Store. Most hosting services will provide online space for file storage and delivery.
You probably have a google account, why not use the free storgae that comes with it on Google Drive?
You should not have any problem creating a direct link to a file on a server, however, most people would be wary of a direct download of an executable file (apk) - and most computers will have an antivirus or executable checker to “control/prevent” such a download. As a minimum, put it in a zip file, but you could provide users with an information page about your app with the direct link.