Absorbers often contain fiberglass, which can shed stray fibers that damage skin, eyes, lungs. I used gloves and a mask when handling the fiberglass and constructing my tube traps. But the fiberglass is typically inside the device wrapped with cloth or similar coverings that would trap most of any stray fibers that come loose. As least in my case it is.
Just some comments (not necessarily to you, but the board):
First...funny memory, the first surfboard I made, I started with an old longboard and filed the edges and pealed off the resined fiberglass to use the foam core—my arms itched for few days from that lesson. The concern is that when you work with fiberglass, tiny pieces can break off and you can inhale them. There's the intuition that the glass is not going anywhere once lodged in your lungs, but it ends up that your lungs clear it pretty easily (unlike asbestos, for example).
But, the only decent chance of this happening is while working with the material, cutting (probably #1), flexing, or crushing it. When it's covered and hung on the wall, there isn't much opportunity. Also, I've read the argument that other materials like cotton and rock wool are actually much harder for your lungs to expel. I don't know, but the argument was convincing enough to consider.
Fiberglass is considered a potential threat, that is sure. But consider that some people work with fiberglass insulation day in and day out in concentrations no one in a studio will be subjected to, and it's still not a slam dunk that it's a major health threat, despite research. If you're making your own panels, it's prudent to wear a mask, make them outdoors or in the garage. After you've covered and hung the panels, it's unlikely they are any threat. Probably similar to worrying about outgassing from plastics in your studio.
Just giving the flip side—I was considered making panels a while back, and got concerned about fiberglass after someone mentioned it, was going to go with rock wool, but after reading more I would just go with Corning 703. Those panels require very little handling anyway, they come in the right size.