Yes, you can retain DreamHost as your registrar
You can set the domain to be "DNS Only" here and will then be able to easily apply your new host's DNS servers.
Panel > Domains > Manage Domains
After the change has taken effect, go back to Panel > Domains > Manage Domains
Click DNS below the domain name
Fill in the fields below Change [domain]'s whois nameservers entering your new hosts DNS servers.
Click Set these nameservers for [domain] !
DNS Propagation will take a few hours, after which your browser should take you to your new home.
Sorry to see you leaving under such unfortunate circumstances