Sure. Have your entire kit powered by a AA batteries. Any connection to the outside world should be either radio-only (wifi/bluetooth) or optical. That way, there's no electrical path that can carry current from a device that's plugged into the wall to your body. In the worst case, you'll have a pair of AA batteries tied to your body, which should be a negligible risk.
AA batteries are a negligible risk when you touch metal with skin. That resistance is very high. Resistance inside your body is much lower -- 100 ohms is typical. If you were to get 0.5v between you arms, you could get unsafe currents.
With electrodes, the current can be /much/ greater than touching metal wires with a finger. Single-digit kilo ohms is typical. The big ECG paddles are tens of ohms, probably.
Another way to think about it -- have you ever felt even a 24v battery? No. Now You know that 9v tingling on your tongue? That's saliva and a tiny contact area. Now think of a large patch of engineered electrolyte can do.
