A traditional silver cell is only used to process solid silver that is at least 90% (sterling silver, e.g.) pure to 99.99%. Like aqua regia is for gold, a silver cell is the final purification step for most silver recovery operations, no matter what items are started with.
Most all silver plated materials have copper or copper alloys underneath the silver. I know of no common cell that will selectively remove silver plate from copper based items, except the strong sulfuric cell that you are presently using. However, what do you do next, economically? Silver stripping was included in the original sulfuric patent but, I've never played with it. The patent holder was a plater and stripping faulty plating was the original intention of the patent
I once developed a cell using cyanide plus a large amount of sodium hydroxide that didn't eat the copper and worked quite well but, you had to keep the parts moving in a tumbler. The silver (or, gold) that stripped automatically plated out on the cathode. The coinage metals, gold, silver, and copper, are found together in nature and have many chemical properties in common. All can be dissolved in cyanide, for example. The high sodium hydroxide in my cell slowed greatly the attack on the copper. This system is, obviously, beyond your scope.
In the books, about the only method given is the super nasty, super dangerous hot concentrated sulfuric plus a little nitric - I think they say 5% for the nitric. No electrolytic cell. All you have to do is immerse the parts. For thin plating, heating isn't necessary. Here again, this process doesn't work economically. It's designed to strip faulty plating off so the parts can be replated.
Most refiners don't want silver plated items. Basically, silver plated copper is considered as contaminated copper. Most silver plated copper only runs 1% silver. Some silverware is higher. Don't buy it unless you pay a lot less than copper price. If you do have a bunch of it, look for a refiner that burns boards, melts all the resulting metals into ingots that run about 65% copper, and then ships the ingots for further refining. He might, just might, pay you a small price over copper market. He always needs cheap copper and can add the stuff to the melt. He often needs extra copper to lower the melting point of hi-temp melting items containing lots of iron and nickel. The big smelter he ships to will pay him for the silver.
