Do I even have a chance of finding a bandsaw that would not be taller than 18 inches (450 mm)?
In the history of the world, it's very likely that someone produced a very small bandsaw at some point, and if so, one will turn up sooner or later on Ebay. If you're really looking for something like that, look for a three-wheeled bandsaw. Two-wheeled bandsaws are much more common, and in that setup the hight of the saw is basically the distance between the wheel axles plus the diameter of one of the wheels, plus a little more for the enclosure, so the height of the saw is directly related to the saw's cutting capacity. A three-wheeled model uses smaller wheels with the third wheel set off to the side to increase the width of the band's path and provide a deeper throat while limiting the height of the saw. The downside of this design is that smaller wheels mean that the blade bends more, which can stress the blade and lead to breaks.
I wonder if this isn't an XY problem, i.e. one where you're asking about the solution you expect rather than the problem you actually have. What capability does a tiny bandsaw offer that you couldn't get from, say, a scroll saw, a portable jigsaw, or a Rockwell Bladerunner (basically an inverted, stationary jigsaw)? A scroll saw, for example, gives you much greater throat capacity than a small bandsaw would, and a handheld jigsaw can handle anything you can reach to.