'Official' Android phones will give you that message if the app isn't from the Google Play Store, and they have a point. As I understand it Google owns the Android name now and if you get an app from anywhere but the Play Store, Google didn't check it out first. Of course, there have been a few apps that were compromised that got through the Google checkout system too, but they are rare.
If you load an app on your phone that you get from an other source it's called '
sideloading'. I've done it with my APTV box and have not had any issues, but I was careful to research the app well enough from the site I downloaded it from to make me comfortable enough to try it. Your idea of trying it on a crappy phone first is good
Please let us know how it works out for you if you do it