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Provided it was within range and you can power it your home wifi router would probably work just fine, you should still have connectivity on your own network, just no internet connection.
I was not aware of Teamviewer needing a net connection to work even in local mode. Give me 5 and I will test that.
EDIT: Yanked the net connection from the router and fired up Teamviewer (Which I use to work on a headless machine in a rack at home) and it connected just fine within my own network, not sure if you need a connection to set it up initially though.
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