In Philosopher’s Stone Professor Quirrel(mort) is shown doing the jinxing (of Harry’s broom) [Ch11], rope conjuration and animation (Incarcerous?) [Ch17], and is ready to use ‘a deadly curse’ [also Ch17] and not a single time is his wand mentioned.
“…and what a waste of time, when after all that, I’m going to kill you tonight.” Quirrell snapped his fingers. Ropes sprang out of thin air and wrapped themselves tightly around Harry. “You’re too nosy to live, Potter. Scurrying around the school on Halloween like that, for all I knew you’d seen me coming to look at what was guarding the Stone.”
Ok. I guess he could’ve cast that spell with his wand-hand while snapping the fingers of his other hand at the same time. But that’s not what is shown. He just snaps his fingers and the spell effect happens.
“Use the boy… Use the boy…” Quirrell rounded on Harry. “Yes — Potter — come here.” He clapped his hands once, and the ropes binding Harry fell off. Harry got slowly to his feet. “Come here,” Quirrell repeated. “Look in the mirror and tell me what you see.” Harry walked toward him.
Again. While it’s possible to clap your hands while holding something (he could’ve been holding his wand between his thumb and side of his palm) it’s very awkward and most certainly isn’t a proper way of casting Finite or whatever.
And finally we have,
“Master, I cannot hold him — my hands — my hands!” And Quirrell, though pinning Harry to the ground with his knees, let go of his neck and stared, bewildered, at his own palms — Harry could see they looked burned, raw, red, and shiny. “Then kill him, fool, and be done!” screeched Voldemort. Quirrell raised his hand to perform a deadly curse, but Harry, by instinct, reached up and grabbed Quirrell’s face — “AAAARGH!”
He was just choking Harry and burned horribly both of his palms; there is no way he could be holding anything at this point yet he raises his hand to perform a deadly curse.
Even after his re-embodiment and return to his true strength, Voldy is never again showed doing anything like that! Why?