Gentlemen why make this difficult. As a former jeweler who regularly refined scrap for customers reslloyed and made misc. Take and weigh your scrap add 4-5 times the weight in pure silver and melt it together stirring thoroughly and while nice and liquid carefully pour it into a metal gallon coffee can full of water causing it to cornflake/ shot. Take the sh0t. Place it in a 12 cu glass coffee pot with 2-3 cups of water and 1/2 cup of hydrogen peroxide. Then add nitric acid very slowly about 2 tablespoons to start with place on low just warming heat and let it slowly react overnight outside away from anything you don't want to rust or if as you mentioned you have access do it in a fume hood. Cover the coffee pot top with cling wrap or press and seal to keep the fumes in. The peroxide will help to keep the fumes down also. Add additional nitric acid as needed in small additions on heat until all of the silver is dissolves/parted. This will leave behind all of your gold in a fine powder at about 98% purity and all of the base metals and silver should be in solution. Carefully pour off as much solution as possible and then filter the gold out through a coffee filter. Dry it and take it to your jeweler to alloy appropriately for the grade if metal you want in your rings.
On the solution. Add salt and you should get a lovely cottage cheese looking precipt known as silver chloride. Store this in an air tight container under a layer of water and if you wish to you can find the appropriate way to convert this back to silver metal elsewhere on the forum. Your jeweler could also do all if this for you in his playing fumehood if he wished to do so simply give him the info. He will also be able to roll the metaled button out flat and thin and cut it into pieces that would dissolve much faster than shot. Good luck to you on this. Sincerely
Ron White