Diamonds are diamonds and they are not always about engagements. It will not look weird to wear 2 diamonds rings. You are lucky! I personally would do a three stone ring with 2 pears on either side, or a halo ring.
How about wearing it as a ring on your index or middle finger? It wouldn't seem so "balanced" with the other ring, especially if the design is dramatically different.
For a right hand ring I think the diamond flanked by two blue sapphires a la Tiffany would be perfect. You have the option of wearing it as a right hand ring, or stacking it with your future wedding band when you want a change from your e-ring.