In theory that would work. Just watch how you are doing things. The switch will handle about everything. Just make sure that the switch knows to use the laptop to get out to the internet. I probably test it with a second computer first because it be easier to debug. Though in all actuallity why not spend the little extra, actually not that much extra when you consider the cost of getting a Lan Adaptor, and just go ahead get a Wireless router/switch? The setup is not any worse and if you ever get Broadband like Cable or DSL you could use that same switch for both your laptop and Wii.
If you are running the cord directly from your Wii to your Laptop you will need to use a crossover cable instead of a regular network cable. Then on the Wii you should mimic the settings on your Laptop, except the IP should be different. You may need to select both the connections and bridge them together.