What are some good prescription sunglasses to take on a deployment?

Some of the APEL Wiley X eye pro will accept the wire frame chemical inserts. Nothing is going to look good, but who are you trying to,look good for, the suck truck guy?

Comfort for long hours of wear without ability to change? Sure.
Being able to see and aim? absolutely
Be able to transition quickly day to limited vis? Yep got it.
Being able to use aiming devices and night vision? Roger.

To give a better answer, I actually was discussing things with the chief of the Army optics lab at BAMC a year-ish ago and he brought some stuff to attention.
Many commercial lenses will be "ballistic", meaning they passed basic tests for "the point blank shotgun" but haven't passed other requirements for the APEL.
"Other commercial eyewear products, even if marked ANSI Z87.1 compliant, do not necessarily meet military impact requirements."
https://www.peosoldier.army.mil/faqs/#eyewearQ5
The inserts look like crap, I know, but they are the approved way for us "disabled" personnel. We aren't working to look good, just to defend. If you want to look good I can happily process your Civil Affairs packet (hehe, had to).
I even asked about polarized lenses, the reason the Army does not use them is because polarized lenses can interfere with screens and stuff.

I'd love to list stuff, but what's on the APEL is what you SHOULD be wearing.