In accordance with the previous 2 entries, allow the third game to follow suit and enable Shepard to holster his/her weapon while exploring. 

First and foremost, Mass Effect is an RPG. One of the key mechanics of many games of this genre is allowing the holstering (putting away) of your weapons to increase immersion and aesthetic of the game. The feeling of drawing your weapon in the time of battle cannot be understated and re-holstering after the battle is won is immensely satisfying; this switches the flow of the game to encourage sight-seeing and discovery instead of constantly looking down the barrel of a gun.

Instead of Shepard constantly holding the weapon at the ready, the previous titles allowed holstering to pull back the camera, increasing field of view and giving more realistic and natural-feeling interaction with the environment e.g. when talking with NPCs. Having the gun constantly at the ready not only looks impractical when not in combat, but also limits the camera movement in exploration. 

According to official reports, this feature was not included in the original Mass Effect 3 release due to limitations in the console RAM (memory). With the later generations of hardware, this should not be an issue. As most of the animations are already implemented in the game when switching weapons, just allow the animation to stop and switch the game state to exploration as it is for many of the other non-combat maps. 

Although this seems a relatively small change, it is incredibly jarring when playing through the trilogy to suddenly not be able to put away your gun. The impact would be substantial to immersion and continuity if it were finally implemented in this remaster.