Some of the safety issues could be alleviated through different product design. For instance -- the charge system is a USB cable direct to the headphones. A fireproof cradle might be one option to handle to at least mitigate for unattended thermal runaway. In fact, a fireproof box in which to charge portable devices might not be a bad product idea.
Most "LiPo" batteries are typically the same chemistry as your "Lithium-ion" but without the puncture and pressure resistant casing. The plastic pouch is the "polymer" part. LiPo batteries are lighter and can produce more current than basically the same thing in a safer standard container.
So yeah, big difference in safety, not really a difference in the chemistry.
The above was explained to me by someone I believe knows what they're talking about. But I may have misunderstood; if I have, please let me know!
LiPo is a subclass of Lithium-Ion (which is confusing), but is a different chemistry. LiPo batteries are typically labelled as such, have either a solid or gel electrolyte, and are packaged in pouches while the rest of the Lithium-Ion cells are labelled LiIon or Lithium Ion, can be packaged in pouches but can also be packaged in cylindrical beakers, these have a liquid electrolyte with the negative electrode being the beaker and the plus being the center typically brought out at a concentric tip.
Manufacturers sometimes use deceptive labeling and given that the form factors are somewhat interchangeable it really is a confusing mess. Unfortunately both chemistries have 4.20V as their 'charged' voltage and 3.0V as their discharged voltages because of the underlying chemical similarities so looking at the voltages won't give you a good idea either.
In the end, the electrode is what matters, but getting to that requires destruction of the cell. One non-destructive way of figuring out if a cell has a liquid electrolyte is to see if you can shift the center of gravity by tilting the cell slowly. If you can then it is most likely a Lithium Ion battery, if you can't then it is a most likely a Lithium Polymer one.
