So, after about six hours work, with a bit of time added on to go and get more staples and screws I have three traps drying in the garage.

I sprayed them with a 1:10 solution of PVA / water, with a drop of washing up liquid added. This seals the fibres in place and stops them drifting around the room. One litre of the solution was enough for the three panels and was applied using a plant sprayer.
Rockwool is not toxic, it is made from er..... Rock so it is chemically stable and inert. However, the fibres can irritate some people with breathing issues like Asthma so you do not want them blowing around the studio. The spraying with the PVA solution drys to form a crust and reduces the efficiency of the panel slightly but not so much that it is a problem.
Furthermore, the fibres can get in your sweat glands and burrow in to your skin. Some people are less tolerant to this than others so care needs to be taken when working with the stuff. Yesterday was cool and humid so not too sweaty, hot and dry days are the worst because your sweat glands will be open. An old builders' trick is to wash your hands with cold water, which washes away the fibres and the cold keeps your pores closed. Yesterday, I moved the Rockwool slabs as little as possible and as the frames are built to their size they did not need cutting. I wore long trousers and a long sleeved shirt too so it was not a problem.
Next job is to wrap the completed framed slabs in fabric.
I have some black fabric which will need bleaching, a black studio is like a dungeon. Neutral lighter colours is the way to go. If you want it darker and moody in there it can be done with lighting.