Does using the wish spell to resurrect a creature killed by the disintegrate spell (or similar) trigger the "stress" penalties of the wish spell?
The first thing that causes me to question this is the general design of it, which is more of a RAI assessment. From what I can tell, wish's non-spell replicating punishment is meant to be a limit and punishment to keep players from breaking the game with repeated and frequent uses of wish to reshape the world and break every other rule of the game with a solid mechanical effect that doesn't put the whole weight of that limitation on the GM's shoulders.
From this perspective, using wish to resurrect someone killed by a spell that explicitly tells them that they have to use wish (or another 9th-level resurrection spell) to resurrect someone is a fully intended system in the game, and thus should not be subjected to wish's punishment for "trying to break the game".
The RAW argument for the resurrection not triggering the punishment is that, if the person has died within the last 10 days, the spell reincarnate only requires you touch a piece of them (resurrection does not have the "piece of them" option), which the dust left behind by disintegrate could be argued to be, and the a new body is generated for them. Wish was used to replicate the spell. Therefore, you are meeting the requirements of disintegrate (wish) and the requirements of the non-punishing wish (replicating a spell) and the requirements of reincarnate (touching a piece of the body). So you should not have a chance to lose the ability to cast wish.
The argument for it not working is pretty straight forward. You are casting wish, invoking the text of the disintegrate spell, not replicating a spell of level 8 or less.
Also, this could seem like it is stepping on the toes of true resurrection. However, true resurrection has a much longer timeframe, does not change the character's race, and does not require the party to pick up all the dust if they can't cast wish before a strong gust of wind picks up. It also only works to counteract disintegrate or other spells with the same effect in the same way that true resurrection does; it does not replace other reasons that true resurrection could be necessary, such as the body being taken out of the party's reach.
The relevant part of the reincarnate spell's description says:
You touch a dead humanoid or a piece of a dead humanoid. Provided that the creature has been dead no longer than 10 days, the spell forms a new adult body for it and then calls the soul to enter that body. If the target's soul isn't free or willing to do so, the spell fails.
The relevant part of the description of the wish spell says:
The stress of casting this spell to produce any effect other than duplicating another spell weakens you. After enduring that stress, each time you cast a spell until you finish a long rest, you take 1d10 necrotic damage per level of that spell. This damage can’t be reduced or prevented in any way. In addition, your Strength drops to 3, if it isn’t 3 or lower already, for 2d4 days. For each of those days that you spend resting and doing nothing more than light activity, your remaining recovery time decreases by 2 days. Finally, there is a 33 percent chance that you are unable to cast wish ever again if you suffer this stress.
Finally, the relevant part of the disintegrate spell description says:
A disintegrated creature and everything it is wearing and carrying, except magic items, are reduced to a pile of fine gray dust. The creature can be restored to life only by means of a true resurrection or a wish spell.
Personally, if this came up in play, I would not include wish's punishment due to the first paragraph; however, with the benefit of foresight, I am seeking a more informed answer.