Thanks for the replies. I think I posted a misleading title, sorry guys. What I want to do is to create a new wallet on a different computer. I'll keep this one as a main wallet. In fact the other computer (the "new" one) is a chromebook, but setting up a wallet on that will be a different story I expect.
Is the disk large enough to fit the blockchain? I have little experience with chromebooks, but I understand that they mainly want you to store data in the cloud, so you can easily switch devices without hassle. If you have enough space to run bitcoin core with a full blockchain, creating a new wallet (with new addresses) is as simple as renaming the existing wallet.dat file. If core starts without finding one, it will create a new one.