Advice about portraying someone with a stutter in a tabletop RPG home game

Advice about portraying someone with a stutter in a tabletop RPG home game Someone in my D&D game is creating a character who is extremely high powered but stays out of the spotlight, using an employee as the face of her operations. To expand upon this dynamic the player wanted to give the character a stutter to explain why they doubted their ability to be the public face of their operations and so relied upon their second in command to do so. I was worried that this might be problematic so I thought this might be a place to check? Is playing a character with a stutter as lacking in social confidence a trope? Is it disrespectful for someone without a stutter to play a character with one?