If you're ok with doing a bit of hacking a Raspberry Pi Zero W is $10 and can run off of the USB port of the laptop.

https://www.raspberrypi.org/forums/viewtopic.php?t=199588

Just tape it to the case with a short USB cable. You can even set up a firewall on the thing so your ancient unpatched Mac isn't pulling its pants down and bending over for the modern Internet scan bots. You could even set up a transparent web proxy on the Pi so the ancient root certs on that version of OSX don't break everything.

Then all you have to worry about is the way out of date web browser not being able to handle all of the new web frameworks. Pretty soon you're asking yourself why you didn't go and find a just-as-cheap and much less outdated laptop instead.

I can recommend the GWU637, with caveats. I spent 3 months in a hotel wrapping up a contract and starting a new job where the hotel wi-fi hated my Mac. Phone - fine. Tablet - fine. Mac? Might as well not have existed. It runs pretty hot and there's no 802.11ac support but often when you need this, that isn't an option anyway. There's an undocumented /menu.asp page that you're almost certainly going to need for anything other than a 192.168.1 network.