Digital or IP?
Digital - change the base extension numbers and ask the customer to go to each phone and dial *36. The first one makes the User disappear from the phone, go to NoUser, but show the new extension number. When you do *36 on the 2nd one, the User comes back to the first phone, and of course the 2nd phone drops to its proper User.
You can also give the Users a Login Code under User>Telephony>Supervisor Settings, use the same code such as 1234. Make a System Short Code of *#N / Extension Login / N*1234. Ask them to go to each phone and dial *# followed by the extension number they want to phone to become. Again, when they do the first one, the 2nd one goes to NoUser, until they get over to the 2nd phone and dial the code. Verify in SSA that the Base Extensions now have the new Users, in Manager change the Base extension numbers, and Merge.
(When we used to do large deployments of digital phones, we would either blank out all of the extension numbers on the Extensions, or put in Placeholder extension numbers. The tech would run cross-connects any way they want, just picking the next available port off of the block, and when getting to the desk log in the phone. When the phones were all up and running, we use SSA to see what User is logged into which Base and square them up in Manager)
IP - have the customer go into the Craft or Admin menu and "Log Out", which is NOT the same as *36 Hotdesk logout - it unregisters the phone from the IPO and returns to the Login prompt that you get when initially installing the phone. Once both phones are unregistered, register them to the IPO with the correct extension number and password.
A mix of 1 digital and 1 IP - blank out the extension number on the Digital extension, Log Out the IP phone via the Craft or Admin menu, reregister the IP with the correct extension number, put the correct extension number back on the digital extension. You will probably have to use the Login button on the digital phone to log it in, I don't think it will automatically come up.