Smile
When you’re singing, try to smile. This gives a sign to those around you that, despite the sounds you’re emitting, you feel good and your intentions are not hostile.
Vocal Exploits
Contrary to appearances, pretending to be a coloratura soprano or a thundering bass is actually the right strategy for people not blessed with talent. The unfortunate experience of hearing such singing will be balanced out by the comic effect, and may also serve an educational purpose.
Sing Often
It’s no secret that you can train your vocal cords. The worse it goes at the beginning, the more you should sing. In other words: the weaker your singing, the more often you should do it. Simple, really.
Listen Rarely
Try to avoid as much as possible situations where you hear your own singing, e.g., on a recording. The shock may be too great, it could lead to a personality crisis.
Reactions to Pain
Try to turn every scream of pain into a vocal exercise. Sooner or later people will stop realizing the difference, and you’ll always be able to explain that actually you weren’t singing, just in pain.
Percussion
While singing, tap rhythmically on things in your surroundings, or on yourself (your thighs, belly, cheeks). The noise you make will drown out your singing, so you can go on for as long as you like.