I want to sing while I work
Why do you like to sing while you work?
Singing makes you feel happy and it's much easier to work when you are in a good mood.
Work is difficult and you should do whatever you need to make it better for you. If singing makes work go by faster it is good.
It is good to do whatever makes you enjoy your work.
Bingo! But please keep in mind not everyone want's to hear you sing, so only do so if people don't mind.