If it's an early unit you should save the reg number in a file then you can refer to it when reinstalled....IIRC it's an option from the toolbar.
Otherwise, if it's a quest, the serial number is in the unit so you connect it and get mapsource to unlock from the unit...I'm not sure about the 26xx range but I suspect it'll be the same.
Backup any routes and waypoints in your Garmin folder though...they should be ok after a reinstall but it doesn't hurt to make sure.