That looks easy enough to do. You could do that with a normal plastering trowel, 11",, 13". It will prove tricky if you've not done this before though, and it's difficult to explain. I normally do this type of ceiling/wall in 2 parts. First, I'll do the skeiling, starting below the radius and working along the join where the skeiling meets the vertical part of the wall. You'll need to prep the skeiling/wall first anyway, Once prepped, (all loose material removed/wall sealed, cracks taped etc), you'll need to pva the skeiling, and plaster onto it while the pva is still wet/tacky. Apply the plaster with the trowel onto the skeiling. Bearing what I have said in mind, go online and type in, HOW TO PLASTER A BARRELED OR CURVED CEILING. Up will come a Youtube video of a plasterer, plastering a ceiling, more or less identical to what you have. Watch it and you will see what is involved. It's not as easy as he makes it looks, so beware.
Going back to your photo's, i'd be very wary of that dark patch on the wall. I think that's "damp". I reckon that over the past 80 years or so, rubbish, dust and other material in the space above the curved ceiling has jammed/gathered at the bottom/edges of that slope behind the lath and plaster, allowing the damp from the outside wall to penetrate through the plaster. In other words, the gap that should be behind the lath and plaster has filled up with dust, sand, whatever, causing the damp patch you can see. Anyone else agree guys. Another thing, if you plaster onto that area as it is, I think you will have problems with it.