Here is what I have done...
Bolt rifle with a hinged floor plate:
Walk to truck, put hat on truck hood or hold hat under hinged floor plate with the same hand holding the rifle.
Unload floor plate over hat, prove rifle safe.
Gather ammo in hat, put hat on, get in truck and go.
Works well with an SKS or Mosin as well.
Lever rifle...
Hold upside down and cycle ammo into hat as above.
Swedish Mauser put safety in the up/middle setting, tilt rifle onto right side, cycle action and catch rounds into hand holding the rifle.
Surely most of you folks wear a hat while hunting.