One would presume that a double-weapon's heads would have the properties of the ring worn on the nearest hand to that end. I like this idea but +1 may not be a sufficient modifier for the ability, as it can be applied to any weapon, even an improvised one, and eliminates the Masterwork requirement. I propose the following alteration:
Ring of Advanced Armament
These rings have varying appearance based on the type of effect bestowed. Each ring grants any one weapon (or end of a double weapon) wielded by the wearer a specific property. Any melee or ranged weapon property may be granted in this fashion, assuming the wielded weapon is of the appropriate type, (IE Keen or Vorpal would only work on an edged melee weapon, Distance would only work on a ranged or (normally) thrown weapon, etc...) The ring's cost is identical to a +(1 + enhancement bonus (minimum +1)) magic weapon with the added property, IE a Ring of +1 Keen Strikes would be a +3 weapon for cost and price, and any edged melee weapon wielded by the ring's wearer (or end of a double weapon) would gain a +1 enhancement bonus and the Keen property.
The wearer may choose which weapon to grant this bonus to, and may change the affected weapon as a free action on his initiative, but only once per round. The affected weapon may not be changed if the wearer is flatfooted, stunned, or dazed.