There is a wandwavium in this planet that makes some islands float, it is really difficult to mine. When it has the appropriate treatment, it becomes a reactionless drive.
This drive consumes electrical energy and it converts in kinetic energy, they use this to create some flying ships. In non relativistic speeds, the conversion efficiency is super high, so it is more efficient than, let's say, an turbo prop or anything we use in modern airplanes. The more speed you have less efficient it is, so I won't need to bother having more kinetic energy in the ship than energy needed to run the drive, like this post about killing machines and perpetual motion stuff.
The origin of the electrical energy to the drive comes from thermal engines, like diesel or gasoline engines, that moves an generator. So without oxygen, the ships won't work as they don't have solar or atomic energy. This way the ships only work on the atmosphere. I suppose they could use an solar sterling engine to create an spacecraft, but, for now, only atmospheric ships.
What would they look like? Airplanes with less complicated drives? A lifting body without wings, like this nasa wonderful ship. Would they even need flaps to control the attitude of the ship if they can accelerate in whatever direction the reactionless drive is pointing?
They will look like an spaceship with multiple drives pointing in different directions so it can accelerate to whatever they want. If i am being too vague i can explain more, I just don't want do bore you to death with irrelevant details. The point is how they would look like being designed to work in a atmosphere similar to our own in relation to other non atmospheric scifi reactionless drive spacecraft.