Yea, I decided to take three of my slings apart to remove every vestige of encroaching and damaging verdigris from in between the brass claws and the leather. It'd grown so much that the brass and leather were pushed apart with some of the rivets starting to pull out of the brass. Those rivets that weren't coming out of the brass were trying to pull through the leather on the other end of the rivet.
So, being a really resourceful guy, I carefully took the claws off and scraped away the green waxy stuff and brushed away all traces of it from the leather with a Soft toothbrush and from the brass claws with a brass wired brush. I used a brass bore brush to clean out from under the hooks of the claws really well. I then cleaned the leather tips with Pecard Antique Leather Dressing and after thoroughly cleaning off each rivet, I tapped each back in to its original hole, allowing the end to re expand in the hole against a bronze anvil. Just had to do it. Now the slings should last another 100 years just fine before they have to be cleaned again. Probably even longer.
One has to know what their doing of course. But it isn't rocket science, so I got through it OK. Besides, having been a handy man for a school district for 12 years, I got pretty good at taking things apart, and putting them back together again after fixing and servicing everything. Wife says that I'm a real wizbang around the house... LOLOLOL
Anyway, I've done it other times since and they turned out good.