If you just want to quickly test your game, why not just preview it or use preview on LAN?
If you really didn't modify any images, disabling PNG recompression will make the export go much faster, then you can just copy the c2runtime.js and offline.appcache up to the server. However if you make a mistake and you *did* modify some images, this could break your project, which is why it's best to do a complete upload each time.