I would ask more questions about the biting. It might have nothing to do with being picked up to go the catio. It might be biting becuase of getting too excited when playing or other things. I would ask their advice on this. It’s also fine NOT to take them out to their playpen.
If it is specifically when you pick them up and have a lightweight carrier, then I’d say get the easier cat out there, and use a treat to see if you can get the other cat in the carrier for the trip. Heavier duty garden gloves might be another idea.
You can avoid getting scratched by a cat by picking the cat up with one hand under it’s chest (cat facing forward) so your arm keeps the cat’s front paws from moving. I use this method when my cats door dart into the hallway and I need tto get them back in. It also makes biting a little harder too.