I would lean towards not touching/worrying about the seed shell. it will not stunt the growth or hurt anything. It's just cosmetic.
The seedling is looking great! And glad to hear it's handling longer in normal air without dropping.
Don't be shy to leave it out longer. If you're around to keep an eye on it, you should leave it out UNTIL it droops, and then put it back under the dome. This is called hardening and will make it acclimate to your grow environment faster than babying it.
Don't forget to keep watering it often since that perlite won't hold it for long.
Try not to get the plant its self or it's leaves wet. That's just asking for other problems.
I hope you keep us updated on the progress!