By default the backup skillsofts are just pure software, and stored on whatever you want (every device is assumed to have basically as much storage as you need, so you could store them all directly on your skilljack, or on your commlink, or whatever.)
If you so wish, you could put them on a datachip which you then slot in (in any device you want). That could be a port on your body (datajack, implanted commlink...) or a connecter on your commlink, which can then send the program on to your skilljack. But by default, it's all stored as software on one of your devices and transmitted wirelessly, if needed.
The skilljack and skillwires themselves are fully internal. I'm not even sure if they can have physical connectors themselves. If so, they would be tiny and easily hidden. Normally external connections would go through datajacks or implanted commlinks, as mentioned, which have bigger connectors as well. But still easily hidden.