dnd 5e – Genie Patron offers the spell Wish as a 9th level option. Do we suffer stress from using Wish?

So I was wondering this based of the new Tasha’s Cauldron update for Dnd 5e. I was flicking through the Warlock section and found that 9th level offers the spell wish for the Genie patron.

I was wondering that since Warlocks have mystic arcanum’s at that level instead of an actual spell slot at 9th level (functions as a spell slot but isn’t actually a spell slot), does it even matter if they suffer the stress of using a wish spell? Because you aren’t really casting the spell, your patron (a very literal genie) is the one doing all the heavy lifting.

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.

And the stress description of Wish 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, the question still remains about whether I can cast wish as a Genie patron without having to suffer the effects of wish because I’m using an arcanum, hence not casting a spell