Do I need to concern myself with being shocked while trying to change the battery?
12V is too low to present any significant electric shock hazard.
The biggest hazard when working on batteries is shorting the thing out. This leads to a massive release of energy which can lead to severe burns. Some precautions that can be taken to reduce the risk.
- If you have any metal rings (or other jewlery) either remove them or cover them with something insulating.
- Disconnect the terminal that connects to the cars chassis (usually the negative) first and reconnect it last.
- Think about what tools you use. Try to avoid using any tool that could short the batter terminals if dropped in the wrong place. If all your tools are bare metal preffer a short tool over a long one.