"The laptop manual says that if I use backup disks they will wipe out all installed programs as well."
Assuming 'backup disks" = 'restore disks' - I think that sentence answers your question.
Though having said that, it might be possible to backup just your Programs Folder (including contents) in C: to an external hard drive; reinstall XP, then restore Programs Folder.
In theory seems OK - but I am not 100% certain of the reality. No doubt someone else will confirm, or otherwise.