IK bones are not active by default and are generally used as targets when content points must be maintained.
UE4 does interpolate by default and can cause the kind of effect depending on the key type being either Bezier or linear. As in the video example I don’t think that’s the fundamental problem your having.
Your basic player model, as in always has been and always will be, is broken down into two basic components as a requirement of having legs move and the torso being responsible for action states (as in aiming, reloading stuff) and needs to be layered so the legs are responsible for locomotion while the torso is allowed to preform an action state while moving.
Start here
Layered Bland Per Bone is what you are looking for.
Zak’s basic animation tutorial has a set up for punching that demonstrates use.
Layer your handgun pose on top of the idle state will not only fix the problem but also change the action state even if the player is running.