Once the electronics are exposed, it is highly recommended that you remain ESD safe. ESD can fry your precious electronics, and pass thousands of volts through components only rated for a few V DC. ESD can sure ruin your day if you are not careful.
Use an ESD mat and wrist strap, and make sure you are grounded for the remaining of the teardown. Make sure your ESD mat is connected to the ground of a nearby outlet, and make sure your house actually has a ground. Consult an electrician if you are unsure.