Hesitation:
* Waver: To fluctuate or be unsteady in opinion or action.
* Falter: To hesitate or stumble, especially from weakness or fear.
* Vacillate: To alternate or waver between different opinions or actions.
* Dither: To act in a nervous or indecisive way.
Giving way:
* Yield: To give way to pressure, force, or persuasion.
* Submit: To accept or yield to a superior force.
* Ceder: To give up possession or control of something.
* Relent: To become less severe or harsh; to give way.
* Capitulate: To surrender or give in to an enemy or opponent.
Other:
* Pause: To stop briefly.
* Stumble: To hesitate or falter in speech or action.
The best word for your specific situation will depend on the nuance you want to convey.