When using some type of rope/twine to hang toys, you want to make sure that it is all-natural, not dyed, and not treated with any chemicals...So you're looking for things like Hemp, Jute, and untreated Leather that is not colored/dyed.
The leather generally will not be a risk of hanging them or of them getting tangled-up, but as far as the Hemp or Jute twine, be sure that you check all of it inside of their cage on a daily basis, and immediately replace any that looks to be fraying and that has lots of stray-ends that they could get their feet, toes, or necks caught in.
Be sure not to use anything fuzzy, as just like the "Happy Huts" they end-up picking the fuzz off of it, which then builds-up throughout their GI Tracts, and this will eventually kill them by blocking their intestines...
The other thing you can use to hang toys, as opposed to twine/rope, are metal chains. Make sure that they are stainless or galvonized steel and are not coated with anything or plated with anything that they can pick off and ingest. Places such as Lowes, Home Depot, and yes, even Walmart sell many different sizes of chain that you can then attach a safe, screw-in fastener (not the spring-loaded, caribiner type). They are sold at Walmart in the aisle that has the Command Fasteners/Strips, next to the Furniture-Moving dollies, pads that they slide on, and right next to the paracord they sell. The aisle is near the tool section. They sell a lot of different diameters and lengths of stainless-steel chains cheaply.