As usual - I'm the rain cloud here - this may not be a good idea if you have transactions affiliated with that customer. I had a client do this to themselves one time, and it was a mess to clean up (edited)
[5:33 PM] That utilize addresses form the customer record
[5:34 PM] That said - you can do a CSV import with the "overwrite sub lists" option to true and upload 1 address. It will remove all the addresses affiliated with it and add 1 new address