What I did in my campaign is to change the wizard's spell list to use the Witch spell list instead, and, voila - instant low magic.
Excellent suggestion.
If you want a campaign with just subtle magic though, even some of the Witch's low-level spells should go. After all, Cure Minor Wounds, Dancing Lights, Flare, Light, and Mending aren't powerful spells, but they are flashy. No one would doubt you were using magic.
At a glance, here are some subtle spells:
Cleric
0-level: Detect Magic, Detect Poison, Guidance, Read Magic, Resistance, Virtue
1st-level: Bane, Bless, Bless Water, Cause Fear, Command, Comprehend Languages, Curse Water, Deathwatch, Detect Chaos/Evil/Good/Law, Detect Undead, Divine Favor, Doom, Endure Elements, Entropic Shield, Invisibility to Undead, Magic Weapon, Protection from Chaos/Evil/Good/Law, Random Action, Remove Fear, Sanctuary, Shield of Faith
Wizard
0-level: Resistance, Detect Poison, Daze, Disrupt Undead, Arcane mark, Detect Magic, Read Magic
1st-level: Endure Elements, Hold Portal, Protection from Chaos/Evil/Good/Law, Comprehend Languages, Detect Secret Doors, Detect Undead, Identify, True Strike, Charm Person, Hypnotism, Sleep, Change Self, Nystul's Magial/Undetectable Aura, Ventriloquism, Cause Fear, Magic Weapon, Message
Even then, some of those spells aren't too subtle (e.g. Sleep, Change Self). Also, since the game relies on certain not-so-subtle healing spells, you may want to create some subtle alternatives. Aid offers 1d8 temporary hit points (and +1 attack, +1 on saves); it can more or less replace Cure Light Wounds or Cure Moderate Wounds.