You can have multiple iCloud accounts on the same device, but one has to be the "primary". Any secondary account(s) you add will support things like Mail, Contacts, Calendar, and Notes (but not things like Safari syncing nor Find My iPhone for that account).
So if your wife does not mind you having her iCloud account set up as a secondary account on your iPad, you could then copy a note from your account and paste it into a new note in her account.
Alternatively, just email the note to your wife (right from within the Notes app) and she can copy and paste the information into a note on her device.