That shouldn't be a problem. All your data is held on the fitbit servers rather than on your One so it's all safe.
Assuming you are using the app on a phone, go into the account section of the app (select your profile or the "ID card" at the top of the dashboard depending on which version of the app you have). There you'll see your One listed in the devices and below that an option to "set up a device". Choose that and select the Versa. It will then step you through adding the Versa to your account. All your data, settings, badges etc will be safe.
You can then choose to leave the One connected so you can swap between them or you can select the One from the devices list and there will be an option to remove it. If you decide to remove it, don't forget to give it one last sync before you do.
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