Actually, i dont know any tools which are working under windows (your PC) and Linux (probably your Online server). I would look for "file splitter" or "upload database in chunks" in Google. I gave it a try and found a PHP-based solution (but did not try to run):
http://www.ozerov.de/bigdump/P.S.: If you like to "upgrade" from 5.6.x to 7.0, this is not an upgrade (or only a small step) for the database, so instead of running big exports/imports, it should be sufficient to simply backing up and restoring the whole "data" folder of MySQL (i.e. MariaDB).