1. Actually, we can have much newer than this. Although the stable installer of TeamViewer 14.2 won't install, the portable will:
https://dl.teamviewer.com/download/version_14x/14.2.56673/TeamViewerPortable.zip
It works fine (and it detects my webcam). According to the official TeamViewer website, version 14.2 is the last one working on Windows XP, so I assume it is also the last one working on Windows 2k.
2. There is a lot of wrong info on the Internet that Opera 12.18 is the last working version on Windows 2k (with BlackwingCat's kernel extension). Opera Portable 36.0 installs and works just fine:
https://portableapps.com/downloading/?a=OperaPortable36&n=Opera%20Portable%20Legacy%2036&s=s&p=&d=pa&f=OperaPortable36_36.0.2130.80.paf.exe
Don't forget to add the flag --no-sandbox to the shortcut target.
3. Google Chrome 49.0.2623.112 also works on Windows 2k (that is the last official working version for Windows XP). But it is a bit problematic to install it:
1st try (failure): The online installer
https://dl.google.com/tag/s/appguid%3D{8A69D345-D564-463C-AFF1-A69D9E530F96}%26iid%3D{4CC3734A-87C1-54C2-D4DA-9B81661C8DDC}%26lang%3Den%26browser%3D3%26usagestats%3D0%26appname%3DGoogle%20Chrome%26needsadmin%3Dprefers%26ap%3Dstable-arch_x86%26installdataindex%3Dempty/update2/installers/ChromeSetup.exe?src=1&filename=ChromeSetup.exe
won't install on Windows 2000 ("This version of Windows is not supported" or something like that).
2nd try (also failure) The portable installer
https://sourceforge.net/projects/portableapps/files/Google Chrome Portable/GoogleChromePortable_49.0.2623.112_online.paf.exe/download
will install, but the executable ChromePortable.exe won't execute (like nothing happens, and the flag --no-sandbox does not help).
3rd try (success ): Install the online installer on Windows XP, and copy the installed folder to Windows 2000, to its original path:
C:\Program Files\Google\Chrome\Application
Then copy the file chrome_elf.dll from Application\49.0.2623.112 subfolder to Application folder, right next to chrome.exe executable.
And that's it. Actually, it isn't. You also need to add the flag --no-sandbox to the shortcut target (and --disable-infobars also comes handy).
4. Skype for Web also works on Windows 2k. Check this article (and my comment there) for more details:
http://www.skaip.org/skype-for-web-on-windows-xp-and-windows-vista