Can I use Hammer of Fighting without sufficient Dark Elixir?

According to this video from the official Clash of Clans channel, you don't need any resources to perform the upgrades. That means, that also the storage makes no difference.

Magic hammers can only be obtained by playing in clan war leagues. At present, there are currently 4 hammers in the game, which can be bought in the League Shop.They are:

1. Hammer of Building: Costs 120 League medals and sell price : 100 gems

2. Hammer of Fighting: Costs 120 League medals and sell price : 100 gems

3. Hammer of Spells: Costs 120 League medals and sell price: 100 gems

4. Hammer of Heroes: Costs 165 League medals and sell price: 100 gems

NOTE: There is a cool down of 7 days after you brought each hammer. i.e If you buy a hammer of fighting today, even though you have enough enough league medals to buy another hammer of building, you have to wait for 7 days

Unlike the magic books, there is no such Hammer of Everything. Also, another difference between the books and the hammers is they don't require ENOUGH RESOURCES to upgrade.If you are going to use Hammer even though you don't have enough resources,you can upgrade the building/troop/spell/hero instantly without using any of your resources.

For more details, see : https://clashofclans.fandom.com/wiki/Magic_Items