Can you use Professor Juniper or Professor Sycamore with no cards in your deck, just to discard your hand?
No, you cannot. Discarding your hand is a cost not the effect, and you cannot play Trainer cards for no effect.
Source: TPCi Rules Team (2017-04-27)

Relevant cards

Note: All applicable cards may not be listed below.
BW1_101
XY1_122