There is little safe about building any of the common types of massless speaker. You need to be very aware of the disadvantages of these transducers before you start any work on them. It is possible to address all of these safety issues and create a perfectly safe end product but it adds a lot to the difficulty of their design.
The most obvious disadvantage. Most designs use quite high voltages - typically a few thousand and sometimes in the 10's of thousands of volts. Not only is there high voltage, but some designs also have the power available to deliver considerable current. If you don't know how to behave when working on high voltage circuitry do not attempt to build or use these devices.
With suitable insulation and screening having high voltage inside a product need not make it unsafe at all. These speakers do need some access to the air in order to create sound, this open area can either be small and recessed enough to be untouchable or surrounded by a grounded metal mesh screen.
All high voltage designs in air have the capacity to produce Ozone. Corona/ion wind designs are particularly efficient at producing it. Ozone is an invisible unstable form of oxygen (O3) which lasts around 20 minutes after being produced before breaking back down to O2. It smells quite refreshing, like a thunderstorm has been through the room, and is invisible. It is highly reactive and in high concentrations will degrade the cell walls of living things, including those in your lungs. An often quoted reference is that designer Nelson Pass successfully damaged his lungs when demonstrating his ion speaker and needed a visit to hospital.
As it is so reactive ozone can be readily catalysed back to O2. Also if there is no oxygen present then no ozone is produced.
Ozone is the most commonly cited form of gas produced, but there is a much more toxic gas produced that is harder to detect and remove.
Plasma arcs are very efficient at producing Nitrogen Oxides (the plasma combines the nitrogen and oxygen in the air), known as NOx and includes Nitrogen Oxide (NO) and Nitrogen Dioxide (NO2) (perhaps some less toxic Nitrous Oxide (N2O) as well). These are far worse than ozone. NO2 is a brown gas with a harsh smell, but at lethal concentrations in air it is not visible and is odourless.
Amongst its effects are that it converts into nitric acid with the moisture of your lungs and eats them away, as well as entering the bloodstream and causing cancer. NOx is one of the emissions that is now restricted on car exhausts by using catalytic converters - you don't want it in your house.
The larger and more powerful the plasma arc, the more NOx is produced and in a small room the levels can build up quite quickly. You can't smell it or see it but it will stream upwards from a hot plasma. I have used a digital NOx meter to detect levels around a large plasma and it is off the scale above the plasma. After 15 minutes concentrations in a small room are above safe levels. Designs like the Hill Plasmatronic used an inert gas to try and get around the gas problems, with no oxygen or nitrogen to combine together no NOx is produced. Klein's Magnat plasma tweeter used an inner silver plated screen to catalyze some of the ozone back to oxygen.
The plasma arcs can emit ultraviolet light. I have measured this on standard plasma discharges with a UV light meter and found it to be at a very low level (barely registering) even on a large arc and so would not find it a worry. On a high current arc discharge the UV levels can be dangerous in the same way as arc welding, causing burning of the retina.
High voltage sources can be used as X-ray emitters. However, there has to be very special circumstances, including specific electrodes and the use of a vacuum, for X-rays to be produced. I have also measured various forms of these speakers with a Geiger counter with no result, but it is something to keep in mind when working with voltages in the 10s of kV.