What is the best way to blend this animations?

I have a couple of Mixamo Store animations, such as idle and gun running, the gun running is holding a pistol, how can i delete the curves only in the arms and make an animation exclusively for the arms and then blend those 2? Is there any way besides animation for the player to hold the gun and create gun bobbing?

You can play animation just on certain bones, by assigning mixing transform (see AddMixingTransform).

You can affect bone proceduraly using some Sin curve, by adding offset on top of animation in LateUpdate function.