Connecting local network using switch and router with just 2 interfaces

Question

I need to connect a very small network (< 5 devices) to another network. The other network provides only a wireless AP.

I was thinking about using an old Linux box with a wifi card and a single Ethernet port as a router/firewall. The Linux box will connect as a client to the wireless network and will route all traffic into a switch. All the end devices will be connected to this switch.

Is this a feasible approach, or have I missed something?