The Otis system uses a plastic-coated stainless cable. It's a nice portable unit that stores in a round zippered pouch about 3 inches in diameter and 2" thick. I keep one in the field pack I take on hunting trips, but don't use it at home.
When using any pull-through cleaning rig, pull straight out the muzzle, not against the crown. A muzzle protector helps, but unless the rifle is a benchrest gun, I wouldn't worry about damage if care is taken.
It's not something I feel comfortable doing and am very careful. The cable is less than 1/8" diameter, so it's easy to not let it touch the crown. The other thing I do is to wipe the cable after each stroke, so it doesn't pick up much primer grit.
Incidentally, I recently cleaned the bore on a 100+ year old Mod. 1894 Winchester with the worst bore I'd ever seen. It was probably shot with corrosive primed ammo and not cleaned for at least 50 years. The rifle was found in that condition and with a loose, cracked stock when a person found it in an attic when they bought the house more than 30 years ago.
I used a bronze brush and plenty of Gun Scrubber, Kroil and Break-Free CLP to loosen the crud. It was very difficult to get the brush through on the first several passes. After each pass, I wiped the rod, sent a wet patch through.
After about an hour of scrubbing, the bore still looked very dark. A patch pushed part way through, could not come back, but had to be pushed all the way. After hours of cleaning, it was apparent that the bore wasn't getting much cleaner. I finally wrapped an old brush with 000 steel wool and ran that through several times and the bore started looking much brighter, though pitting was evident.
Next, several tight patches with GB Bore Paste back and forth. Then more bore cleaner and CLP. The bore looked pretty good, considering, but I was concerned that it wouldn't shoot well. I cleaned the chamber with a Remington 7400 chamber brush then patch.
A friend loaded some very mild cast lead bullet loads with about 7 grains of Unique and left some primed cases and 150 grain jacketed bullets for me to load. I glued a piece of .010" shim stock to the head of a case and tried to chamber it, but the action didn't close, so I figured the headspace was okay.
Next, I took some cast bullet lube and smeared it on a patch and ran it through from the muzzle end, figuring that would lessen friction when the first shot was fired. I don't know if it helped, but I fired a lead bullet and it struck the target at 25 yards without keyholing. Another round was fired and printed about an inch away from the first shot. Primers and cases looked normal, with no signs of excessive headspace or chamber roughness.
I then loaded some mild loads of jacketed 150gr bullets using A-2230 and fired them without incident. Three shots went into an inch group near the top of a 6" bull. All shots made nice round holes!!
I'd read test results recently where bores could get really bad and that scrubbing doesn't hurt them as much as once thought. Crowns were deliberately damaged and still the bullets flew straight. Still, I wouldn't deliberately damage a bore/crown, but remain impressed that this particular rifle seems to have some life left in her.
I cautioned the owner to clean carefully after 5-10 rounds and to protect the bore with Break-Free CLP after cleaning.