Gillie uses a nebuliser and has never had any problems. My suggestion is: take the documentation and don't panic. Airlines are used to shovelling people with all manner of infirmities onto aeroplanes, But speak to the cabin crew when you get on the plane if you will need to use the device in flight; they may suggest that you go to the toilet to do it. They are not waiters and waitresses - they're highly-trained professionals, and have probably seen everything. They can use defibrillators, CPR, deal with the dead, help nervous fliers, evacuate a plane in ninety seconds, assist at births and so on. The important thing is to smile and be nice and explain a problem. They will do everything they can to help.
The important thing to remember is that you are not unique. Millions of people use nebulisers. Relax, and enjoy your holiday. I once flew to Rhodes with a very painful slipped disk. I walked around the plane most of the time - which would be potentially suspicious behaviour. Four hours of agony. When I explained why to the cabin attendants they were immensely sympathetic, and even gave me an extra-legroom seat for landing.