How to transfer Skype Contacts and Conversations to a different computer?

I believe it's automatic. So when you log on using the other Mac all you do need to do is load the application on the new mac.

Within a number of days the history where you have talked to your friends will be synced. That will only happen when they come online. Messages on their local history will then be transferred to you. So I don't think you should do anything but load Skype on your new computer

Regards
Jacques