I'll keep this short because there are many more factors involved in business recovery...
If you make the site an identical copy of production and suppress the routes or advertise them to your ISP with a less favourable AS path, managing and monitoring them remotely will be painful.
I imagine over time you will want to store backups there and copy configs and make copies of production changes in your warm environment, general maintenance. If you have an identical IP scheme, you need to start NAT or some other mascerading process. Most applications don't like this such as SNMP.
My personal view is DR must be hot to be effective which means you will eventually need to apply unique IP's and use the DNS flip.