The cones and chains may be somewhat fiddly to deconstruct. Sometimes the cones are stuck to the horsehair with a gum substance. I have found heating the cones with a hair dyer has helped loosen the gum to enable removal of the cone.

As for the chains being removed, maybe be a problem as the only ones I have seen is where the chain is sewn into the horsehair and then glued. I had some old wrecked tassels and took one apart and I would say that if you want to use the original chain, then you will have to replace the horse hair.

All in all I think you could easily remove the cones but try to match/ substitute the tassel chains