It looks like you are correct in assuming compatibility with the new graphics card. You should be able to just swap the cards around however, Dell have supplied you with the bare minimum power supply. If you replace your graphics card without upgrading the power supply you risk burning out your current power supply (possibly damaging other components).
So I would recommend getting at least a 300 watt power supply or go for the graphics card's recommended 350W there shouldn't be much price difference.
I will also state that it is not a guaranty that the new graphics card will burn out your current PSU just a risk. Personally I've had a bad experience doing this with a Tiny PC so I would go for a PSU upgrade (I was lucky, I didn't loose any hardware).