What to do with the neutral in a 240V 2-pole hot tub disconnect?
You never switch the neutral, well, &quot;never&quot; is a strong word, sometimes some special generator installations switch the neutral, but almost never should you switch the neutral, just the 2 hots.  I like your idea of putting the GFCI inside to protect it.
To connect the neutral, there is usually a small bussbar you can land those on. If your new hot tub doesn't require a neutral, just cap it off in the disconnect.
Your idea about just passing the neutral thru the disconnect unbroken works too.
You got this!