Actually, I always recommend developing completely on a local computer.
Good software development includes proper software development environments, which means that you should be sure to develop locally, and only deploy to a production environment when it comes time to do a software release.
So yes, I developing locally will definitely work. I would develop locally, on a local database and local webserver. When it comes time to build, the simplest thing you could do is write a script which FTPs/SCPs everything to your webserver.
In terms of database builds, if you have no shell access, at the very least you could do is use something like PPHPMyAdmin (if you are using MySQL). I am pretty sure there are similar tools for PostgreSQL as well.