dnd 5th – Can magic users control arcane energy other than the spells they can cast?

Situation that arose:
A Level 1 assistant decides to interrogate a goblin. He wants to "shock him lightly with electricity" to wake him up. The only spell he knows is Shocking Grasp, but he does not try to cast the trap, he tries to summon a much weaker form of shock, just to bring the creature back to consciousness.

My question is – to what extent are magic users in tune with weaving? Can magicians only summon magical energy via their known spells, or can they manipulate energy at will to produce smaller RPG effects? I think it's more likely that wizards are able to do that, but not wizards. Are there official documents explaining these relationships better than the PHB?