The key here is to make sure you have the means to reinstall after deleting what's on your machine now.
If you DO have a disk, then proceed with the uninstall, then reinstall from the disk, then use Software update to bring iWork up to the most current version for your OS.
If you purchased from the Mac app store, the individual applications should be listed in your purchases. If so, go ahead with the uninstall, then reinstall the apps you've purchased by downloading them again from the app store. App store purchases may be installed on any compatible device assigned to the same Apple ID. There is no serial number involved.
You will have a disk only if you purchased the retail box version (with either the single or family licence). This does not require a serial number.
Regards,
Barry