I have an extra golden axe and an extra silver axe.
If you still need them, I can give it to you.
The golden axe will not break and the silver axe will almost always get you a tree stump with a special pattern.
Hint: You need 3 chops to fell a tree, use the golden axe 2 times and the silver axe for the last chop to extend the durability of the silver axe (it is breakable after 34 - 38 hits based on my experience).
Extra: The golden axe you can get after buying 50 tree saplings (not bushes, bamboo shoots or flower seeds) from Lief (who runs the gardening store in your main street). The silver axe you can get it from island gift shops for 8 medals (quite rare).