If you're attuned to a Sword of Vengeance, you have disadvantage on attack rolls made with other weapons.
Does that include the natural weapons of a druid in Wild Shape?
If you're attuned to a Sword of Vengeance, you have disadvantage on attack rolls made with other weapons.
Does that include the natural weapons of a druid in Wild Shape?
The rules for the Sword of Vengeance state :
While attuned to this weapon, you have disadvantage on attack rolls made with weapons other than this one.
As discussed in this question, wild-shaping does not remove the curse from your character, as it is inflicted to your character as soon as you attune to the sword :
This sword is cursed and possessed by a vengeful spirit. Becoming attuned to it extends the curse to you.
Natural weapons are weapons, meaning you will have disadvantage when attacking with them while under this curse.
While the question Can a druid use Wild Shape to get rid of a cursed item? explains why a druid cannot use wild shape to physically drop a cursed item, that is not what is relevant in this question. Rather, the question here is whether the "has no effect" clause of wild shape would suppress the disadvantage.
When a druid wild shapes, there are three things that can happen to their equipment:
You choose whether your equipment falls to the ground in your space, merges into your new form, or is worn by it.
Because this is the druid's choice, it interacts with any features of the curse that affect the druid's will. The Sword says
As long as you remain cursed, you are unwilling to part with the sword, keeping it on your person at all times.
Thus, the druid cannot choose to have the sword fall to the ground. However, either having the sword merge with the wild shape or be worn by it keeps it on the druid's person, and depending on the form chosen, having it merge is likely the safer and more practical way of retaining it.
While the sword is thus merged, wild shape says (emphasis mine):
Equipment that merges with the form has no effect until you leave the form.
The sword has:
While attuned to this weapon, you have disadvantage on attack rolls made with weapons other than this one.
But having the sword merge will mean that it, including its curse of disadvantage, temporarily has no effect on the druid. This might be enough to suppress the disadvantage. However, the sword also says:
Becoming attuned to it extends the curse to you.
It is the meaning of 'extends' that is unclear here.
It could be that 'extends' means 'Once you have attuned to the sword, its curse has been extended to you and exists on you independent of the sword'. If so, then the disadvantage will persist in wild shape, because even if the cursed sword itself is suppressed, the effect of the curse is still active on you. This is the case with something like the shield of missile attraction. Once you have attuned to the shield, you can set it down and pick it up at will, but you are still cursed regardless, and even if you were in wild shape the curse would persist.
However, it could be that the curse is actively generated by the sword, and as such an ongoing effect it is suppressed while the druid is in wild shape. If 'extends' means 'While you are attuned to the sword, its curse is extending to you', then you will not have disadvantage using your natural attacks when in wild shape. This would be similar to demon armor. This gives you disadvantage in attacking demons "while you are wearing" it. When it merged into you wild shape you would not be wearing it, and thus its effects would clearly be suppressed.
Because the sword does not specify whether the curse is actively maintained by the sword or exists independently of it after attunement, the DM will have to decide how to interpret the effect of the sword. A good test would be to consider what would happen if banishment was cast on the sword. The item description says that this drives away its vengeful spirit and makes the sword into a normal magic weapon. However, it does not say whether banishment ends the wielder's attunement to the sword or ends the curse on the wielder. Would banishment be sufficient to end the curse on the druid, or would they still need a separate remove curse cast on them because the curse had been extended to them independent of the sword? If your DM can answer that question, they will know whether the curse is suppressed while the sword has merged with the druid's wild shape.
This sort of rules lawyer approach to your game is really robbing everyone of a lot of the real depth you can get here. You are the DM, so it's YOUR world, and these are questions that you need to address. And in the old days, magic weapons had a 25% chance of being intelligent so you could just ask the sword how it feels about it and let it decide.
First, how did this cursed item come about? Was it made for a purpose? What is that purpose? Why does it want vengeance? Against whom? Why does it impose disadvantage when using other weapons? Is it because it does not you to ignore it? Is it jealous of the other weapons?
Let's assume the latter case. If you pick up a rock and throw it at someone, does it get jealous of the rock? If you slap someone is it jealous of your hand for not holding it in it? What about eating? Can you use a knife to cut your meat normally, or does it cause disadvantage on cutlery? Does it cause disadvantage on sewing? theives tools? These can all be used as weapons! So, I think this is a situation where the GM should make a ruling based on the needs and wants of the sword. I see no reason a sword of vengeance created by creator A should work identically to creator B. Maybe they followed a different recipe or substituted an ingredient. Quality control doesn't have to be perfect in the middle ages!
In animal form, it is likely impossible to hold it, but if you merged with it, and abide by the "vengeance" portion of the curse, are you not using the weapon? I mean, it merged with you, and you attacked with a natural weapon and couldn't actually hold the sword anyway. Does the sword care?
So, do what works for your world and your players. If there is some specific reason you have this sword giving disadvantage to this player, maybe some deed you want them to perform to remove the curse, then in that case, I would say that the disadvantage functions in wild shape. If this is a random roll treasure and a minor inconvenience they'll fix in the next town, then the sword should be pretty happy and not jealous of natural weapons.
Use this as a narration tool to enrich the story. The rules are whatever works best in that story.