I've used white spirit/turps substitute successfully for softening wax polish it works well as does genuine turpentine, but its much cheaper. Here are a few observations over the years and also I'm a working chemist so can comment on chemistry and safety. I dont think you need the expense of genuine turpentine, unless you like the smell.
1. M
ost important is don't heat the turps or solvents as they are highly flammable. Instead melt the wax first over a bain marrie or glue kettle as
@Phil Pascoe recommended pour into a jar (old jam jar) then add the solvent or solvents, and then stir in the solvents with no heat applied. Be very careful with warm solvent as it can explode if near a source of ignition. Also see the exposure limits for the solvents in point 5.
2. Beeswax and canuba wax are food safe. Canuba wax comes from the Brazilian palm tree.
3. White spirit can be quite variable in the oils contained in the solvent so select a well tried source.
Good White spirit should be odourless. In the UK there is a BS standard BS 245 or German DIN 51632 these ensure they are suitable as solvents for washing brushes etc and also get consistent results for plasticising wax. This standard means the toxic (sweetish smelling) aromatic oil has been removed and also the more volatile kerosene smelling oil fractions has been removed. So quality white spirit whilst cheap (it comes from an oil refinery by the tonne), should be odourless. If it smells sweetish or kerosene I would be careful not to breath and only use for cleaning brushes. White spirit is not ideal for thinning paint as its not that volatile, but is great for softening wax.
4. Turpentine has a strong distinct 'pine' smell, this comes from its chemical structure it has a double bond (also called unsaturated hydrocarbon) and its shape mean that the nose can distinguish its distinct smell. Some people like this smell in furniture - antique effect.
However its can overwhelm food so if in contact with food or children's toys, its better to use odourless turps substitute.
5.
Toxicity, Turpentine is more toxic than white spirit (to the BS or DIN standard) the exposure limit in the USA for
Turps is 100ppm for an 8 hour day and
500ppm for white spirit (called turps substitute). EU will be similar if not more stringent.
6. For first coating, I've read that some people add boiled linseed oil to the mixture in the ratio 1/3 turps(subs) 1/3 boiled linseed oil, 1/3 wax. The boiled linseed oil give it a darker appearance and brings out the grain better. I've not tried this myself. you could just give the surface an oiling before waxing.