web shared is less secure. i've never used it and i've never had a problem with any ds wifi games. i've had some trouble getting mario kart to connect to routers (i've tried many). after its connected i can game for hours with no problems. my theory is that the mario kart wifi code just sucks.
wep open
channel 1, 6, or 11.
802.11b
turn off any range enhancing features
your NAT firewall could be causing issues, it has for a few different routers i've played with.
make sure you aren't blocking the ds by its MAC address within the router
good luck!
-another world