Would it be offensive to say "The Ormerod School educates handicapped children from South"? Should I use "Disabled children" instead?
This is a highly complicated matter, heavily dependent on what country you are in, and what attitude you expect the audience to have. However, handicapped is frowned on by the disabled community everywhere in the English-speaking world that I'm aware of. The pitfall is whether you should say "disabled people" (or children) or "persons with disabilities" (or children with disabilities). The first is social model language, and the second person-first language. The former is preferred by organised disability movements in Canada and the United Kingdom, and the latter in the United States, though of course both have their adherents in the countries that prefer the other. The explanation as to why each is preferred by its adherents is, I would say, beyond the scope of this site.