Would a silver helmet count as a silver weapon for bypassing a Lycanthrope's DR?
Of course it would.
A suit of adamantine armor used as an improvised weapon bypasses DR because bypassing DR is a property of adamantine.
This falls under the subject of what types of weapons are effective to damage which types of items. From the Core Rule Book:
Ineffective Weapons: Certain weapons just can't effectively deal damage to certain objects. For example, a bludgeoning weapon cannot be used to damage a rope. Likewise, most melee weapons have little effect on stone walls and doors, unless they are designed for breaking up stone, such as a pick or hammer.
Keep in mind, this gives only a couple examples, anything beyond that is entirely a GM judgement call.
Additionally, it is certainly not unreasonable for a GM to rule that a large piece of armor is generally ineffective as a weapon, because it is beyond unwieldy.
Additionally, say you are trying to break down a door. A conventional bludgeoning weapon is able to do such a thing, because it has all of its weight concentrated in a very small area, giving a very high pounds-per-square-inch ratio. An Adamantine Breastplate has its weight spread over a very large area, producing a very low pounds-per-square-inch ratio.
Yeah, I would have made the same call as your GM, but for different reasons. A piece of armor just has too much of its weight spread over too much area to make an effective bludgeoning weapon against a trap door. Perhaps if it is medium or heavy armor, and thus comes with gauntlets, I would allow you to try by punching with gauntlets (if armor comes with gauntlets, which medium and heavy armor does, you are always armed, as gauntlets are simple weapons), but I would not blame your GM for disallowing this either. Punching a metal door is generally not going to do anything but hurt your hand, no matter what you are wearing on it.
Ok, and what are you trying to damage with the trap-door?
Well, this is going to depend on the size of the trap door. If you use an object as an improvised weapon, you compare it in weight and size to an existing weapon, and determine what size category and handedness it is. If it is so large, that it would most reasonably be considered a large, two-handed weapon or larger, then it would be impossible to wield at all, as per the rules on inappropriately sized weapons.
Also, how exactly did you get this adamantine trap door off its hinges, which presumably are adamantine also? If you don't have an adamantine weapon to begin with, how would you bypass the hardness of the trap door and its hinges to detach it from the floor?