There is no way to just go push ios updates remotely without a third party application, if that is what you meant. To update ios you have many options. You can go to each iPad and download the ios. Or show the students how to download the ios themselves. But if I were you I would get an iPad cart, and go to few classes a day, collect the iPads during that period and use apple configurator application to download the updated ios. Then give the iPads back. If you have any more question just give me your school e-mail address and I will help as best as I can.
-Hope this helps.
Which grade levels are you working with? I ask because we are currently working with 9th - 12th graders, and we do iOS updates by e-mailing students instructions and asking them to do the updates at home by a certain date - mainly so that our network is to overwhelmed with traffic. Students who did not have Wi-Fi at home, did the update on campus. Believe it or not, that worked great.
Currently the only iPads not locked down with restrictions enabled are Administrators and teachers who have their own Apple IDs. That is no problem because they can do their own. It is the K-6 that I have the most issues with because I have to unlock them, do the updates and then lock them down again.