Since Warlocks have Mystic Arcanums at that level instead of an actual 9th-level spell slot (functions as a spell slot but isn't actually a spell slot), does it even matter if they suffer the stress of using the wish spell? You aren't really casting the spell; your patron (a very literal genie) is the one doing all the heavy lifting.
The Mystic Arcanum feature description states (emphasis mine):
At 11th level, your patron bestows upon you a magical secret called an arcanum. [...] You can cast your arcanum spell once without expending a spell slot. [...] At higher levels, you gain more warlock spells of your choice that can be cast in this way [...] You regain all uses of your Mystic Arcanum when you finish a long rest.
The last paragraph of the the description of the wish spell states:
The stress of casting this spell to produce any effect other than duplicating another spell weakens you. 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.
So can I cast wish as a Genie-patron warlock without having to suffer the stress of casting wish because I'm using a Mystic Arcanum, hence not casting a spell?