Technically the mod adds alternatives to all three parts of the arrow's crafting recipe: flint can be replaced with horns, sticks with blackroot/mallorn sticks and feathers with swan feathers.
In the real world, the only alternative to feathers I can think of is plastic - which obviously does not belong in Middle-earth.
If you're having a hard time obtaining arrows, just buy them from traders. It's much easier than hunting for birds.
Just make a chicken farm. It doesn't take long to get 10 stacks of feathers with a blessed sword.
Make an enclosed area that they can't get out of. Put at least two chickens in the pen and right click with seeds to breed them to make more, or, since they're chickens, just collect and throw the eggs to make more. When they become adults, you can kill them for feathers and chicken.