I found a way to hold it that works for me.
Rule #1: do not use the pick stylus. Use a normal one. Right when I switched to a regular stylus my accuracy improved.
Rule #2: have the strap as lose as you can make it, and hold the DS in your lap. This will allow your fingers to align more naturally on the buttons without cramping your hand from holding it tightly in an uncomfortable position. Plus having it in your lap it's less likely to drop.
Rule#3: strum towards/away from your body rather than left/right. I found this to be a lot easier on my wrist.
To activate Star Power I usually just blow on the system, and I wear headphones so I don't disturb people around me ....