Yep - as suspected the default route to the internet is via 192.168.200.1 - the wired interface.
The solution should be
route add -p 0.0.0.0 mask 0.0.0.0 192.168.1.1 metric 1
This should add a persistent default route via the wireless. Give it a go and let us know.
---------- Post added at 19:42 ---------- Previous post was at 19:41 ----------
This page has a description of the route command on XP.