You could use Comgenie's File Manager if
1. The file you're uploading isn't 4 gb by itself. You could put 2gb (or 1gb... I don't know how much your usb can hold) on your usb, copy it, delete it from your USB, and then copy 2gb more to your usb, then copy that to your PS3, delete, etc
2. You can afford an 8gb USB stick
But if you can't do either of those, I don't think there really is a way to do this without an FTP server

sorry.