We see Force Persuasion used in the Original Trilogy and every time, the persuader has to speak the words out loud to persuade the victim(for lack of a better word) . I was wondering if it was possible to use Force Persuasion without the persuader having to speak out the words, just using the Force.
Nope. You can use it wordlessly, at least according to the new (Disney Canon) novelisation of RotJ; Return of the Jedi - Beware the Power of the Dark Side
The leather-faced guard and another even tougher-looking one who might be his brother — or sister? — have selected Luke as the first course and push him toward a plank that has extended from the side of the skiff.
One of the guards — guided by a Jedi mind trick — decides to remove Luke’s handcuffs.
Elaborating on Richard's answer: Using the Force in Star Wars is just like casting spells in Harry Potter. Strictly speaking, you can use any Force power with just your mind. However, body gestures (and speech) help in painting the mental image of the desired action and effect. As Luke demonstrated, you can manipulate objects telepathically using just the mind, but using hand gestures normally makes it easier. They are like training wheels on a bicycle.
It's all about making a Force power easier to use by reducing the amount of conscious mental effort needed and more effective by making it more accurate in doing exactly what you want it to do. It's easier to fight with a lightsaber if you're holding on to it and let the Force simply guide your motions rather than having to visualise the lightsaber's orientation, bearing, speed and coordinate position while having your hands tied up. It's easier to verbally instruct a Stormtrooper to unbind you, leave his weapon behind and walk away rather than "program" it directly into the trooper's brain using brain-code.