Can i give a APK file to a "stranger"?

I want to test my android game on different android phones. I planned to make a thread where people can send me a pm and i will give them the android file. Then they need to tell me how the game look on their device.
Im just worried, that if i give them a download link to the file that they can take the file and upload it to google playstore, or do what they want with it.
Is it possibly that it can happen, is it a good idea to make a watermark on the screen for the test?

Check out Google Play Alpha/Beta.