See with the school how they would prefer to have the items packed, or of they are indifferent, have a nice little back sack for your kid.
As I mentioned, there isn't all that much difference for the kits, and the reason in part is because it is a child's kit, which must be kept simple. Even the kit for the woods can be modified to have more in it if need be.
Also, because the elements of survival, or survival priorities, are the same, but you simply must adapt to a different environment. The kit I modified from the Children's Survival Kit geared for the woods.
Work with the age and capabilities of your children, to adjust the kit accordingly as well.
I understand that you may feel that in an urban center having a kit
filled with a bunch of stuff may seem overwhelming and unnecessary, but
things do not always work out the way we think they will.
The government under the right conditions will not have the capacity in manpower and resources to go deal with your local schools emergency situation.
An example is after a large earthquake. The debris in the streets, the damage to water mains and electrical infrastructure, as well as the overall situation with many injured people etc., will mean it could take awhile to get to your child's school to render assistance.
As with other emergency scenarios, including a 72 hour kit (go for a 5 - 7 day kit), it is to be able to deal with your predicament until help can finally arrive.
A kit doesn't need to be overly complicated or take much room at all. When it does become a problem, it is usually due to a lack of experience and knowledge in building a kit.