Maybe just contact them.
Tell them if they let you use their symbol, you will make an ingame link to their website's charity page.
Just don't mention that your game might be about decapitating zombies, robing banks, or dismembering soldier in creative ways with a Robot tank.
Be sure to let them know you are only using their symbol "as the global icon for healing, and humanity"
They might allow games like "Little red ridding hood's retro-gothic trip though the zombie infested cemetery, to buy a baby-blood slurpee from 7-11"
You could also claim "Comedy fair use" (satire?). I think this is how M.A.S.H. was able to use it.
I would avoid it all together.
Just draw a Giant Red-syringe, or a red-BoneSaw on a white background like RockStar would if they where threatened.