Using a funnel to fill a burette is pretty standard practice. As potassium manganate (VII) is oxidising and harmful, you definitely don't want to get any in your eyes; you're already wearing eye protection, but if your head is below the level of the burette, any spills are more likely to get into your eyes. Also when you're actually filling the burette, if it is above eye level you'll probably be reaching up, meaning that you are potentially pouring the liquid with much less control.
Sodium ethanedioate is solid, and dissolving it in water shouldn't produce any hazardous gases. So a fume cupboard probably won't help much. The question has asked for safety precautions other than eye protection, so wearing gloves would be a good idea