No, no kaboom. Pressure cylinders are required to undergo hydrostatic testing regularly, depending on the type of material and any specific manufacturer recommendations. Generally steel cylinders are on a five year hydrostatic test requirement, while carbon fibre and lightweight cylinders go on a three year cycle. You can check for this date on the cylinder itself; it will be stamped into the neck, and each subsequent test date will be stamped there.
Airlines do not choose their oxygen equipment because it's somehow tougher and able to be dropped. The requirement that an airline use their own equipment is because it's been under their approved maintenance program and control; it's a known quantity and quality. There is no determination made or able to be made regarding a foriegn or unknown piece of equipment brought on board. You could check the hydrostatic test date, but you have no way of knowing if the cylinder has been purged with each filling, how many fillings it's had, or it's maintenance or history life. You have no way if it's been kept dry, or if it suffers internal corrosion due to moisture from improper filling or storage.
Your King Air probably uses a standard steel E cylinder under the litter. The risk of the cylinder exploding is a non-issue. With oxygen cylinders, you should be far more concerned about the regulator attachments. Break these and the cylinder may become a missle with a mission. Your smaller portable bottles, often stored at the back of the airplane to use when onloading and offloading y our patient, are a far greater potential for damage, especially from dropping.
You're probably already familiar with the requirements to crack the valve slightly and open it slowly, to never position yourself over or adjacent to the valve, to refill it slowly, to avoid proximity to petroleum products (which can self combust in the presence of pure oxygen), etc. These are far more important to your longevity than wondering if the cylinder is going to go kaboom. It isn't.