You could try your own solvents--acetone, Goo Gone, paint stripper /thinner etc. However, without knowing the fibre content, there is a risk that you will destroy the fabric. Nylon and acetate are probably the most sensitive to chemicals and I don't imagine your shorts are acetate, but it would be a disaster if you shredded the fabric on your shorts.
Polyester and cotton are pretty safe fibre types to work with, if you decide to do it yourself. However, your dry cleaner would probably tell you off for not starting there--if you use your own chemicals it might alter what they are able to do. You didn't mention what kind of paint caused the damage but be sure you take the details to the dry cleaner.
If you try your own chemicals, work from the back with an absorbant towel /cloth at the front, and try to push the stain from the back of the fabric through to the cloth at the front. Hope this makes sense. You don't want to push the stain further into the fabric.
Next step would be to dye them orange (brown? dark grey? ) I think you would probably regret trying to cover orange with white, but I think Lexi has a very creative idea.
Good luck with you quest!