Laravel, dump-autoload without Shell Access

Run composer dump-autoload locally. Then, in your hosting site, you can update two files, autoload_classmap.php and autoload_static.php, manually in vendor/composer folder. I prefer to copy and paste the added classes from local to the hosting server.

You dont need shell access. Artisan includes a dump-autoload function. You can just it via a PHP call within your app:

Route::get('/updateapp', function()
{
    \Artisan::call('dump-autoload');
    echo 'dump-autoload complete';
});

Edit: just noticed you wrote "composer isn't installed on the server anyway". Not sure what will happen - try the command above and let us know.

If it doesnt work - then just run composer dump-autoload locally - then upload your new autoload.php.

As a side point - is there any option to switch servers? You going to keep running into various issues if you dont have command line & composer access. You could just use Forge and spin up a new server on DigitalOcean, Linode etc in less time than it would take to fix this issue :)