Dropping pre-order bonus weapons in DX: Human Revolution?
Solution 1:
Most of the pre-order/DLC/booster-pack weapons can be purchased from some shops if (and only if) you have the booster-pack activated, so if you discard the one you are given you will be able to purchase another later.
The Wikia notes that for the double-barrel shotgun:
This weapon is available straight away in the booster packs that come with the pre-ordered version of Deus Ex: Human Revolution and purchasable from merchants later.
There is also a DB Shotgun on a high shelf inside one of the security stations outside at the docks.