Password protected video
What about an app like Android Video Protector? It is advertised as being exactly what you're looking for:

How to protect video files on Android Platform?
Android Video Protector Solution contains two software, there are Android Video Protector and PPVM Video Player. Android Video Protector is a video encryption software running on Microsoft Windows Operating System, it uses a password to encrypt the video you hope to protect, and supports 4 types encryption modes:

Device Binding, One Device, One Password
Non Device Binding, All Device, One Device ID, One Password
Non Device Binding, All Device, One Password
Encrypt video only

How to playback the encryption video on Android Platform?
Because the video is encrypted, the general video player can't playback this video, PPVM Video Player is the player running on
Android Platform and supports playback the encryption video. it
firstly check the playback password, which can be generate using
Android Video Protector, after complete the password authentication,
it will playback the encryption video.

I have no idea if these programs are reputable or if they work. The Android app is a direct download from their website (not the Google Play store) - proceed with caution at your own risk.