You can simply configure IP forwarding on the linux box to forward the traffic from the XP host to the wireless router. You should indicate which distro you are running. Many like SuSE have a check box you can select to enable IP forwarding. On others you need to add "echo 1 > /proc/sys/net/ipv4/ip_forward" to a startup script in /etc/. You also may need to modprobe the "nf_conntrack" kernel module before ip forwarding will work. Also, you need to configure the routes. Routing works by forwarding packets based on the subnet that the NIC (or wireless) interface uses.
For IP forwarding, you want each network interface on a separate network or subnet. Then configure the routes, either through a GUI config utility (probably the same one you use to configure your device) or using the "route" or the "ip" command.
I used to use the wireless interface on my laptop to give my desktop internet access via the wireless router.
I subnetted the LAN so that the wireless network was on 192.168.1.0/255.255.255.128 ( the wireless interface was 192.168.1.100) and the desktop was using the 192.168.1.128/255.255.255.128 network ( its NIC used 192.168.1.132 ).
Code:
Wireless network(wireless): 192.168.1.0/25
Desktop network (jesnet): 192.168.1.128/25
Laptop wireless interface: 192.168.1.100/25
Laptop NIC address: 192.168.1.130/25
Laptop default gateway: 192.168.1.1
Desktop eth0 interface: 192.168.1.132/25
Desktop gateway: 192.168.1.130/25
Route commands for Laptop:
route add -net 192.168.1.0 netmask 255.255.255.128 dev wlan0
route add -net 192.168.1.128 netmask 255.255.255.128 dev eth0
route add default gw 192.168.1.1
Route commands for Desktop:
route add -net 192.168.1.128 netmask 255.255.255.128 dev wlan0
route add default gw 192.168.1.130
I also had a printer and occasionally an old laptop for testing on the jesnet subnet (192.168.1.130/26). I also changed the router's config for the wireless network. The IP address stayed the same but the netmask changed: 192.168.1.1/255.255.255.128.
So to do what you want, you don't need to install or use bridge utils or use NAT on the Linux box if your wireless router is a NAT router. You simply need to configure the subnets/gateways/routes.
Lastly, because you have only two network devices using a wired connection, you can connect both computers using a cross-over cable, eliminating the need for a switch or hub.