You definitely need qualified coaches, otherwise it would be massively unsafe.
As you say, most schools do not have qualified coaches which is why there needs to be links between schools and local clubs. With my daughter's school, we (the local club) are offering to help out with coaches if required.
You can do a course to learn the basics of introducing contact over a couple of evenings and there are lots of evening courses to learn the basics. The entry level proper coaching award is the England Rugby Coaching Award which takes 7/8 months to complete.