Why would you want to melt the gold or silver into ingots?
The places I have sold gold and silver pay a lower price for non-standard ingots because they have to be sent off for an assay, and may contain foreign objects hidden in the center... Sure doing a specific gravity test is helpful for detecting ingots with a lead core but still... I wouldn't melt anything into ingots without a very good reason. It makes trading more difficult.
The only reasons I can think of for melting are.
1. The scrap doesn't have any markings and it would be more convenient to handle in ingots.
2. You are planning on making something from it yourself.
3. You need to hide the origin of the metal.