I know all of us have cleaned with bleach to kill the germs. But try this, try Rubbing Alcohol, not only leave a shine but leaves good smell. Like Bleach it has that strong smell and I know you don't want the kids to smell that.. Try Rubbing Alcohol and you will see a difference. Rubbing Alcohol leaves a shine and kills germs but has minimal smell to it
I use rubbing alcohol for a lot of cleaning - it works great on any kind of glass or mirror. It shines chrome. I also use it to clean the inside of refrigerators. I agree the smell dissipates almost immediately. It's a great cleaning product and comparatively inexpensive. A little goes a long way.
Also, a mixture of 50 percent water and 50 percent white vinegar would do the trick. It is totally safe for kids, not poisonous at all (which rubbing alcohol is). It gives off a vinegar scent, but this will dissipate after 15 mins to half an hour. Cheaper than rubbing alcohol too!