There are several core forms specifically designed for low field radiation. Pot cores and toroids immediately come to mind.
So by choosing a toroid, you have correctly selected a good core shape.
A simple trick to visualize stray fields is to obtain very fine iron powder. On you inductor under test, apply the rated DC current with the aid of a laboratory supply.
Place the inductor on the iron powder. Any material that sticks to it are because of stray fields.
De energize the core in a separate area, and weigh the amount of iron powder that was attracted to it.
Then compare a different core.
This is only a qualitative test, but can help you visualize the relative amount of stray fields. For EI-cores, it is surprising the amount of material which is attracted to the gap.