The right interpretation is your second one.
The Sage Advice (pag 8, first column) says
Can a rogue/monk use Sneak Attack with unarmed
strikes? The Sneak Attack feature works with a weapon
that has the finesse or ranged property. An unarmed strike
isn’t a weapon, so it doesn’t qualify. In contrast, a rogue/
monk can use Sneak Attack with a monk weapon, such
as a shortsword or a dagger, that has one of the required
Since it is stated that an unarmed strike is not a weapon, the rouge can not use its Sneak Attack.
Moreover, the above writings remarks that the Sneak Attack feature works with a weapon that has the finesse or ranged property: hence you can not use a martial weapon to do a Sneak Attack.
Looking at other sections of the SA, one can find also the following, under Can you use green-flame blade and booming blade with
Extra Attack, opportunity attacks, Sneak Attack, and
other weapon attack options? (pag 17, emphasis mine):
Third, these weapon attacks work with Sneak Attack if
they fulfill the normal requirements for that feature. For
example, if you have the Sneak Attack feature and cast
green-flame blade with a finesse weapon, you can deal
Sneak Attack damage to the target of the weapon attack if
you have advantage on the attack roll and hit.
Again, it is remarked that the requirements of the Sneak Attack must be met, including the finesse or ranged property.