I like to include the peels when I make applesauce to get the benefit of the nutrients in the peels*, but I strain them out afterward for the sake of texture. This is a messy, sticky, time-consuming process, and it makes it harder to maintain a chunky texture to the applesauce.  It occurred to me today that perhaps I could make a sort of bouquet garni with the peels in a cheesecloth pouch and then just lift that out afterward (maybe give it a quick squeeze). Would this work? Would the cheesecloth change the flavor of the sauce? Any other concerns I should watch out for?    *I do know the difference isn't huge, but old habits die hard. 
Induction tops are usually glass or ceramic, and they will scratch over time no matter what pans you use. Cast iron works very well on induction, and is inexpensive. It is heavy though, if you drop one on your induction top you could crack it.   