First of all,providing your skype username to other's is usually not an issue. But most people don't konw how,but providing your skype username is a simple way to get your IP address. Most people on Neopets related forums do not know how to do it.
To provide your skype from NOT getting hacked,first of course don't have simple passwords. Which could leave to bruteforcing.
Second,don't let people know who are on your contact lists. Don't know what kind of skype purchases they made,etc. Real simple stuff like that. Keep those details safe and to yourself only.