Hi Matty-
For the tinker toys to be safe for your rabbit you would need to know exactly what type of wood(s) they are made from and check to see if its bunny safe. If they are painted even if “child friendly” that doesnt mean they are safe for rabbits. Idealy you want to stay away from woods that are painted and have varnish because they can make your rabbit sick.
I have brought home planks of wood from Home Depot that are unfinished and lay them in the floor and my buns just sit and gnaw on it. lol You could always find or make a small structure from untreated wood so that you know its safe.
I have emailed companies before to find out what type of wood they used and typically they wont give you a straight answer because their toys aren’t meant for animals to chew on. So they would rather not take a chance of getting in trouble. I called a popsicle stick company (which BTW-are very BAD for your bunny; the wood splinters and can pierce thru organs and cause damage) once and they danced around my question refusing to give me a straight answer.
Hope this helps!