Prince Rupert's drops are an example of a tempered silica glass component: its surface has been cooled more rapidly than its interior. Tempering of glasses is important because it lends toughness to the glass, i.e. an ability to resist fracture under load, which explains why a drop can be hit with a hammer and survive. Silica glass, as is common with other ceramic materials, exhibits unstable crack propagation when its fracture strength is exceeded by its stress state. Unlike with most alloys, ceramics exhibit very little, or no, plastic deformation. When they reach their elastic limit they fracture. So if you stress a silica glass component too hard, it fractures rapidly and all at once.
A glass component may be tempered by cooling its exterior more rapidly than its interior so that there is a non-uniform residual stress distribution in the component. Specifically, because the exterior solidifies first, its density increases and volume decreases first, drawing material outward from the interior. Then, as the interior solidifies with less remaining material, it pulls inward on the exterior. The resulting stress state is tension in the interior and compression in the exterior.
Cracks only propagate when there is a tensile stress across the crack. If there is a residual compressive stress across the crack, it will remain closed unless stressed in tension. Because the compressive stress must be overcome before the crack opens, it takes a greater tensile stress to propagate a crack through a tempered glass component than an un-tempered component. If such a crack propagated past the neutral-stress surface between the exterior and interior of the component, the crack tip would be in tension due to the residual stress state of the interior. Such a crack would begin propagating in an unstable fashion as all of the residual stresses are released, resulting in an explosion of glass shards, as they all undergo elastic recovery from the non-uniform stress distribution.
From all of this, it should be apparent that a "perfectly" spherical, tempered glass component is theoretically possible, as it is only required that the exterior of the glass cools more rapidly than the interior to obtain the required non-uniform stress distribution, while maintaining the desired shape. A combination of gravity and viscosity are the cause of the tail in a traditional Prince Rupert's drop. Therefore, removing each of those components, such as with a drop formed in free-fall by free-surface surface-tension relaxation of a "floating" blob of glass, can result in a sphere of viscous glass. Relaxation may take a long time and the glass must be kept viscous the entire time. The next step is cooling the sphere rapidly without disturbing its shape, which is admittedly difficult. Spraying it with fluids would cause ripples in the surface, and submersion would require moving it infinitesimally slowly, which would cause the wrong kind of non-uniform stress distribution. Exposing it to the vacuum of space might be sufficient, but I haven't done any calculations of the radiated heat loss.
The desired setup would likely be a radiation oven in the vacuum of space, with a blob of glass floating in it, with no relative velocity. The oven melts the glass, which relaxes into a sphere. The oven is turned off, the door is opened and the oven moves rapidly away from the sphere. The sphere emits radiation, cooling the surface more rapidly than the interior (or so we hope), and the glass is tempered, resulting in a Prince Rupert's Space Drop.