As with most things in Skype, it works but it is buggy and the interface is very inefficient.
As suggested, you can add your new account as a contact to your old account, right-click on your new contact and click "send contacts".
Here is where we have a typical Skype poor interface decision. You cannot "select all" so you have to manually go down the list and check each checkbox individually. I had 300 contacts and it took about 15 minutes.
Next, we have another typical Skype inefficient interface. When you receive your contacts at the new account you have to manually click "Add to Contacts" on each one individually. Not only that, but the click action takes you away from that screen so you have to manually click back each time. This took me about 25 minutes. So, Skype wasted 40 minutes of my time due to lack of a "select all" button.
Finally we have a typical Skype bug. You can import your phone contacts (i.e. contacts that have no Skype Name, only a phone number) but Skype has a bug where it loses the name you assigned to these contacts. So, if you had a contact "John Smith" with phone number 777-123-4567 your imported contact will not be named "John Smith" it will be named "777-123-4567". So, instead of a bunch of named contacts, you'll just have a bunch of random phone numbers... completely useless.
It's too bad Skype doesn't care enough about quality or user experience to actually make this work properly.
