Unlike in most games, grenades are often slow to deploy and that can enable the enemy the means to survive. That usually means shooting you or causing more problems. So, in Operation Downfall as opposed to most games you can simply grab a grenade with your right hand and remove the pin with your teeth, thus preventing the need to holster your rifle or other long-arm. You can also of course release the spoon prematurely which will start the fuse, and again unlike most games the spoon separating is also physically visible. A nice perk of this I imagine is being able to tell when a grenade is live or not, probably in the coming multiplayer.
A handgun can be used when your held long-arm is empty, simply grabbing it with your right hand if it's loaded you can start shooting it immediately. This makes it a crucial backup weapon if the enemy is within a range where reloading may prove deadly, whether from being within grenade range or another proximate effect. To reload the handgun one must reload their rifle, then select the handgun as it's own weapon which permits the user to also then use their left hand to reload as well as fire it steadied.