The small, thin straws often served in drinks are for stirring not sipping. After gently stirring the drink without making clinking noises with the ice, discard the stir stick as soon as possible.
If you are seated at a table, place the stir stick on the bread plate.
I have attended many cocktail parties where I have observed someone standing with a drink in one hand while continually stirring the drink to the beat of the music with the other. Please don’t let me catch you doing this.