I think I have it, but I have no idea how to script (or adjust a soldier addon) for it.
Just like you can put one weapon down (on the ground or to a vehicle) and pickup another, you can make a soldier addon with a backpack (that's a backpack in the addon code, not necessarily actually visible).
Then through the action menu you could (for example) select:
"Put away M16A2 take Binelli Shotgun"
and then when you have the Shotgun, through the action menu, you can do the reverse.
Now whose gonna code a new "Soldier addon" for me?
I need a volunteer!
You there!
Yes, you!
The odd-looking one, Step Forward! ;D ;D ;D