Be aware that there are several feats that give you access to other classes' cantrips. If your player is willing to start as a human, he can take one of those feats immediately without disturbing the game balance at all.
Or he can wait until level 4 and take such a feat, no matter what race he is. (Spell Sniper is great for warlocks for many reasons, by the way.)
Or he can take a level of wizard or sorcerer as soon as level 2 and gain several wizard or sorcerer cantrips. (I mention sorcerer because it meshes better with a warlock's ability scores.)
Or if he is willing to play a high elf, he gets a free wizard cantrip of his choice, no matter what class he chooses.
I would suggest presenting those options before setting a precedent of blurred lines among the various class features.