I don't think any Thinkpad 600 series had built in Wifi.

The fastest 600 (600X) is limited to 288MB RAM, a P3-650 processor, and an old pre 3D Neomagic video chip. Not sure you can Skype with something that old.

https://support.skype.com/en/faq/FA10328/what-are-the-system-requirements-for-skype

Windows XP Service Pack 3

Windows Vista

Windows 7 (32-bit and 64-bit versions supported)

Windows 8*

Processor At least 1 GHz

RAM At least 256 MB

Additional software DirectX v9.0 or above