It will not break the game
From my own experience, when my party was level 3-4, we lacked a healer. Only my character had access to a healing spell, Healing Word, and nobody had potions at all. As a result, when we faced off against the BBEG, a party member died in the attempt.
The DM then gave us an item that would allow me to cast Cure Wounds at level 1, thrice a day, consuming no spell slots. It would regenerate the used charges at dawn. The result: one of our party still died on our next boss encounter. He died from failing 3 death saving throws.
The trouble with low level is, even with access to magical healing, you're all still a small sack of hitpoints running around, and you have to be smart about using your resources if the villain the DM throws at you is actually cunning. The long game of attrition we had to go through before we even saw the BBEG forced us to use all of the magical healing we had outside of spell slots.
This isn't to say you can grant players magical healing for free whenever. The item must not be the equivalent of a healing cantrip, or else it makes all hit die obsolete. A DM of mine would add "healing stops" in his dungeons when we played because he knew the sheer amount of attrition he gave us would make us need those, to have enough power left for the big boss battle. By "big", I mean these are dungeons that took around 3-4 sessions to complete, with a big XP reward at the end.
This is to say, if you see your party in sore need of extra healing, do not be afraid to throw some at them in a controlled manner. A Cure Wounds wand that goes off only X times a day is controlled and not game breaking.
They will outclass the item soon enough
Just as how a wand of Magic Missile isn't going to be relevant at the higher levels, a wand of Cure Wounds will not stay competitive with your players' other abilities at the higher levels as well. Specifically, if one of them picks up the Healer feat, or the natural spell slot progression means they can do better healing than the wands, or the players start picking more defensive features -- as what happened in my game -- you will find that the wand of Cure Wounds will not see as much use as it used to in the lower levels.