If the LAN port and the WAN port are both routed ethernet ports, then you are good to go. One port becomes the next hop address for all hosts on the 172.16.32.0 subnet sending traffic to the 172.16.0.0 subnet (I'm assuming you subnetted this B into multiple C's), and the other port becomes the next hop address for all hosts on the 172.16.0.0 subnet sending traffic to the 172.16.32.0 subnet. So for instance, the WAN port gets the IP address 172.16.0.1/24, and the LAN port gets 172.16.32.1/24. If this Linksys is really a dual-ethernet router, and automagically injects connected routes into its routing table like it should, then everything will work.
Is there an Internet link somewhere in this configuration? If so you need to make sure the default route or gateway of last resort on the linksys points to the IP of your router connected to the Internet. Also if said Internet router is configured as the default gateway for the hosts on one of your subnets, you need to either change the hosts to use the Linksys as the default gateway, or else put a static route on the Internet router for the remote subnet. Choice is yours.