PG--You can actually play the chord as a single note--just put your index finger on the D string, second fret-and do the rest as I mentioned--if you are a bit sloppy, your index finger will fall across the other strings anyway, and if you give a squeeze, you might get lucky and get a few extra notes-if not, no biggie--

I used to give this little bit (with the one finger) to my beginners--you don't even need the pinky--if you want, just play with the D string Second fret, and hammer on your middle finger to the fourth fret--mindless boogie at it's most basic!!!!!

My thought is that when you move the C chord up, you create something related to a D and Bminor--

If I wanted to really pick on you, I would tell you how to play that D chord with the F# on the low E string as a closed position chord that you can take all the way up the neck--(it'll only hurt for the first few times you do it!)