I'd use glue, the special stuff they use for vinyl floors, in an ideal world. It's perfectly safe if left to breathe for however long is recommended, and tucking up the sides means wee is less likely to get underneath it (have a look in an office or linoed public loo next time you're in one!). Unfortunately, because of the type of flooring and previous fixation techniques used for my wendy house lino, I think I might have to use staples... If you do use glue, I would check the fixation to the type of wood (timber or composite) before proceeding!