Wordpress Domain Cloaking

I have a Wordpress installation on Dreamhost that needs to display a domain from GoDaddy.

This is a project for a client who bought their own domain, and we are developing and hosting their website including an e-commerce store. They do not want us to host the domain fully on Dreamhost, so I need to be able to cloak the subfolder in which the Wordpress install is located so that it appears to be completely at their domain.

Currently, GoDaddy is set up with domain forwarding with masking so the domain shows up on the address bar and does not change. The links still show our domain and that is what I need to resolve.