How much different is the new design? Is it just a manner of the look, or are there significant differences in the flow and features of the new design? Are they using the same database setup, or did things change between the old and new versions? Should they be able to use either site to do the same things? For instance, if they create a record on the new site, should it show up on the old site?
If there's minimal change, the easiest thing might be to just punt and run the old site as it's own website. Put a big link on the new site that says "If you want the old site, visit oldsite.example.com". It's usually nice to figure out how you can socially engineer the customers to want to use the new site instead, and also tell them that the old site will be disappearing permanently at some point.
I'd be very reluctant to infect a new system with hooks to support an old system you want to move away from.