You could perhaps try the local Family History Society or records office to see if they can suggest any possibilities for a military education in the area. Another long shot of course but if there is an obvious school there may be records or they may have fed through to a specific regiment.
However, he may just have gone to a normal school but was funded by the army - perhaps due to his father or other family member being military. Have you looked into that possibility?
Do you have him in 1911 census? If he is at boarding school or an institution this may help.
Do you have a marriage certificate? Was he still serving when he married as this sometimes gives army details.
And another long shot. Was there a funeral report or obituary when he died? This may make reference to his service.
Sorry - lots of long shot areas for further research - but I think you may be in for a long search to find anything concrete

Milly