You CAN dupe Cryoshear
I just finished helping a friend dupe a few Cryoshears on multiple operators of his a few hours ago. It was his first Cryoshear (and he got really lucky with the correct affinity) while also searching for my second Cryoshear case so we could recreate the same dupe method we did on mine the first time.
The duping process is very similar like duping exotic-named guns. In this case, you'll need to find another exotic weapon case with a Cryoshear in it and have a friend hold the case. I recommend doing this with a friend because before you exfil, you'll need to remain in their squad so that you can respawn back near your friend's location and you won't have to travel far from where they're holding the case. I'm also not sure if an operator you want to dupe to needs to already have an exotic rarity melee upgraded beforehand. But since my friend's operators already did, I can't confirm whether that's required.
Pick up the Cryoshear you just acquired from the box and have your friend hold the case while you exfil with the weapon so it's saved to your operator. Next, join your friend's lobby again using the same operator with the Cryo-acquired weapon. This time, you hold the case (don't swap anything yet) so your friend can step away for a moment to move around or fire their weapon/throw equipment/etc. to reset the inactivity timer and avoid being kicked.
Have your friend hold the case again. Drop the Cryoshear you want to dupe into the case, then force close your game without exfilling. Switch to a new operator you want, rejoin your friend's lobby, claim your duped Cryoshear from the case, and exfil. You can repeat this process as many times as you want in the same lobby by taking turns holding the case so your buddy "can stay active."
I wish we had recorded it as proof, but we got excited when it worked that we completely forgot. And for reference, we've been doing this via Falkner because your operator can sometimes exfil by confirming Falkner's body, or fly over nearby to Zone 2's exfil LZ quicker.