My current thinking on spellbooks is that they do not contain spells per se, but the necessary formulae to power the spells you know; astrological tables, mystical symbols linked to season, day and time of preparation, that sort of thing. I think of cantrips as being the simplest magics, the ones that don't need complicated formulae, so you don't need a spellbook to prepare a cantrip. You do need to prepare it, however, or at least power it. There are two ways to do this:
- Bleed power from a similar spell you've prepared. You can use the Bluelight cantrip if you have Light or Continual Light currently memorized, or use the Firefinger cantrip if you have Burning Hands or Fireball memorized. I'd require a saving throw or Intelligence check modified by the memorized spell's level to prevent losing the spell, perhaps with a risk of the full spell being cast uncontrollably (maybe only under extreme stress, though; no accidentally Fireballing your firewood on a campout.)
- Prepare the cantrip on the spot, if you have an open spell slot. Thus, a 1st level magic-user who has cast a Sleep spell already can spend the next rest period to prepare a cantrip, storing it as if it were a 1st level spell. Because this doesn't require a spellbook, a 1st level magic-user can remain magically relevant for an entire excursion.