If your app is working locally, then you should have all the files you need. Then upload them via FTP. I do this quite often.
All composer does is pull in files from remote servers. Once those files are locally on your computer you don't need composer to do anything else... just upload all of the files including the vendor directory composer creates.
Is your application up and running on your local computer? Have you run computer on your local computer to install the dependencies of your project? If not, that is the first step.