Getting schools to sign up to a STEM competition

This is a trial for me, as I don't know the best way to do this. So suggestions on how to achieve the goal is helpful. My client is a charity running a competition for Primary and Secondary schools and students aged 9-17. Entries have to be in English. So schools with good English and STEM interests. The final is next July in London. The target is to get 200 entries from at least 15 countries (excluding U.K. and China). They would like to reach schools in Africa, American, South America, Europe (not U.K.), Central Asia, India/Pakistan and Australia to register for the competition. I would like to ask if there are freelancers in these regions who can find lists of these schools and email them to join the competition. Perhaps your own schools would be interested. There is very low fee available.