A fun way to use paint without the mess is putting the paint in a Ziploc bag. Make sure the Ziploc bag is securely closed all the way and to not use too much paint.
Your child will have fun playing with the squishy feel of the paint, and you can make it an educational tool as well by teaching letters.
Afterwards, the paint will not go to a waste as you can use it later for finger painting. Or you can keep it in a safe place (in another Ziploc or container for storage) to be used in the future.