tcopitho's post and advice is right on

I really only have a few small things to add.
My Milo is one who freaks out completely when carried if I try to hold/restrain him, and unless I keep him from seeing the ground moving right underneath him.
In other words, I have to let him lay on either my arm or my shoulder --shoulder works better because my body is keeping him from seeing the ground moving right under his face; if he's on my arm, I'll put my hand under his head to shield his view of the ground underneath.
I think the more you try to "hold" him in your hands, the more he'll feel restrained and claustrophobic --especially when moving. Once you've got him out of the tank and to whatever area you intend for your interaction, put him down by you or on you, and let him move around at his own convenience as much as possible, so he can learn to relax a bit. Like tcopitho said, putting down a few things he can crawl into/under, maybe even a towel or t-shirt in your lap, will probably help him relax quite a bit, and will let him relearn that being taken out of the tank isn't always about being restrained and afraid. And hopefully over time, with a lot of gentle patience on your part, he can learn that being outside the tank means good things happening: treats, food, and interesting things to explore.
I like to use a couch for these purposes; it's a smaller area where your presence can be fully felt by the skink and it's easy for you to keep the skink within reach, but still allows the skink some space to crawl off and over your lap to either find something interesting or something to hide under/behind.
When they start squeezing into areas where they might be hard to keep an eye on, or when they look like they might try to crawl off the edge, calmly pick them up and put them back on your lap and just let them go again; once they start to feel less stress and more curiosity, you'll notice a huge change in how they react to being picked up --it's the best feeling in the world when they no longer stiffen and fight being picked up, but instead seem to accept the handling.
If your skink is one who just darts off in any direction without regard of running off edges, maybe get someone to help you with blocking off his path, so that it'll be easier for you to stay calm and keep all motions around him slower.
Again, shorter sessions while he seems stressed out, but once he relaxes and gets into checking things out you can keep him out for longer periods.
If baths are stressful for him, I definitely suggest stopping them. If you feel you need to get dirt off of him before handling, maybe get a washcloth wet with warm water and just hold it while letting him crawl through it --he may even like being wrapped up in it for a while...
Breeder and keeper of Meraukes from 2010 to 2022.