Yes! It is one of the safest countries in the world. The OECD gives the country a 9.0 of 10 on safety (http://www.oecdbetterlifeindex.org/topics/safety
/). This is just a little behind the UK and Canada but ahead of the United States. There are about 510,000 privately owned guns in a country of about 50 million. That means 0.01% of the population privately owns a gun.
One measure of safety in this country is the fact that middle school and high school kids walk home from their hagwons, on their own, at 11pm to midnight all the time.
Just be smart.
No country is flawless, so in order to protect yourself from Korea's few inevitable bad eggs, use the same awareness and knowledge you use in your home country.
. Be aware of your surroundings. Don't let the general safety lull you.
. Stay away from dark alleys.
. Don't incapacitate yourself with alcohol.
. Escort each other home.
Concerns for your safety are always valid.
However, it is not likely that North Korea will attack the south while you are teaching.
Western media tends to get more worked up over North Korea than the South Koreans do themselves.
Remember, they live with this every day. If they aren't worried, you don't need to be either.
There are also political dynamics (which we're not qualified to speak on at length) that would make it unwise for North Korea to attack South Korea. Not only that, South Korea sends the most aid out of any country and so its not in the North's best interests to bite the hand that feeds it.
Here's a great article written by one of our teachers in Korea on the topic: http://www.huffingtonpost.co.uk/april-salchert/north-korea-south-korea-anxiety_b_2858119.html
Register with your country's embassy when you arrive. Then, in the very unlikely event that North Korea does something to put you in danger, the embassy will know how to contact you.