Seriously?
All addresses inside the LAN should be in the private, possibly custom, subnet ranges.
If they're not then the LAN has bigger issues.
You can also have more than a pair of DNS servers, you could configure eight or more. (Internet hostname resolution, and Office LAN hostname resolution, with a back-up for each, and maybe an alternate for each, with a backup alternate for each).
Traffic that can only be routed via the Internet, if there is no gateway on the Office LAN, will never be routed via the network interface that lacks a gateway. 🙂