Should be no lore-breaking problems for you here, as Dwarves have a long history of cutting down trees. In fact, when the dwarves were first made by the Vala Aulë, Yavanna foresaw that “many a tree shall feel the bite of their iron without pity.” (The Silmarillion, Chapter 2: Of Aulë and Yavanna). So chop away my friend and feel good about it!
"I do not love the bright sword for its sharpness, nor the arrow for its swiftness, nor the warrior for his glory. I love only that which they defend," Faramir in TTT by JRRT.