In order for a Skype resolver not to have your current IP, you will need to enable this setting on ALL your Skype clients. This protects you from everybody but your contacts. If you find one of your contacts is obtaining your IP (even without a resolver), then attacking you, you will need to remove them from your contacts.
I have tested this out and it does work. However you may not see a change until your ISP issues you a new IP. After enabling this setting you can call you ISP and have them change it, or possibly change out network hardware or your hardware address to get issued a new IP when your modem power cycles. Most ISP's change your IP at least once a week.
If it still works after doing this, how come it could not resolve my current IP by my Skype name?
More than likely it is resolving a history of your old IPs. There is no way to purge that from a 3rd party site. As soon as you get issued a new random IP by your ISP, it should no longer match.