If you don't really want an applet you can do it server-side in PHP by using this something like this to let the user select a folder:
<?php
$connection = ssh2_connect('host', 22);
ssh2_auth_password($connection, 'username', 'password');
$stream = ssh2_exec($connection, 'ls -a --file-type');
?>
Just parse the $stream
variable to identify the folders (the ones ending with /) and present them in a table.
I guess this solves your problem. If you want the user to upload a file just put a simple file upload field, Once the user have selected a folder and uploaded a file in a temporal location in the server just move it with SSH too:
<?php
$connection = ssh2_connect('host', 22);
ssh2_auth_password($connection, 'username', 'password');
ssh2_scp_send($connection, '/temporal/filename', '/remote/filename');
?>
For getting this working you need to have enabled SSH2 libraries for PHP in your server.