Rather than just sticking a strap on your DSi, you could use something with a bit more function: A dual strap/charger.
The Thrustmaster T-Strap is a mere cord that plugs in the back of your DSi. But through the remarkable engineering of a little plastic piece thingie, the cord creates a loop when not plugged in that's suitable for slipping around your wrist. Additionally, the T-Strap converts the DSi's proprietary connection to be USB-charging compatible. So as long as you've got a USB hub available, you can charge your DSi.