No, zone of truth does not work on corpses.
Speak with dead targets a corpse:
You grant the semblance of life and intelligence to a corpse of your choice within range, allowing it to answer the questions you pose.
A corpse is not a creature, it is what is left after the creature dies. And according to an unofficial Twitter ruling by Crawford, the corpse is actually an object.
Zone of truth only targets creatures:
Until the spell ends, a creature that enters the spell's area for the
first time on a turn or starts its turn there must make a Charisma
So a corpse, even one under the effects of speak with dead would not be affected by this.
Another unofficial twitter ruling by Crawford supports this for this exact combination of spells:
Zone of truth works on creatures. Speak with dead works on a spirit in a corpse—not a creature.
Even if you did, for some reason, consider a corpse to be a creature, it still would not force you to reveal information honestly. Firstly, it only has an effect if the creature fails a charisma save (you'd have to decide what this was since the corpse is not a creature anymore and doesn't have stats). Secondly, the corpse doesn't even have to try to answer the question helpfully. There are plenty of ways to be vague or cryptic while still being technically truthful and thus obfuscate the information given to the PCs.
Of course, in-universe, there is not necessarily a reason that the corpse would automatically consider the PCs enemies and avoid giving them truthful answers. So, if you want them to avoid answering be sure they have a reason in-game to do so.