If I have a wired network with a DHCP-enabled router, do I need a wireless access point or a router to give wifi access to the office? Do all wifi routers have a mode for reverting to access points if the routing isn't necessary?
Generally, yes. Most wireless routers will work as wireless access points just the same. You will probably want to disable the DHCP functionality, though, and use a regular LAN port for your upstream connection instead of the WAN port.
How many people are you talking about giving access to? Many consumer-grade wireless routers will start misbehaving after a dozen or two concurrent users.