Is it possible to add compatibility with other types of string like Silent Gear's sinew fiber?

You can change the crafting recipe with a datapack to accept different items via a tag.
Then you just have to define what items you want in that tag, also via datapack.

You can change the crafting recipe with a datapack to accept different items via a tag.
Then you just have to define what items you want in that tag, also via datapack.

that. indeed.