If the majority of the solution is silver nitrate/ copper nitrate, any halogen added such as chlorine or chlorides will form silver halides or silver chlorides in the solution.
Just a little chloride or halide in a silver ionic solution will show up well as a large white cloud and if enough a white fluffy conglomerated clouds of silver salts precipitated from solution, which is very beneficial in testing solutions because it shows up so well with such a small amount of the halide or the silver...
With a limited amount of chlorides added they will be removed from the solution along with their silver bonded ions, either as a milky-looking precipitate or small fluffy white clouds of silver chloride (which can be somewhat reduced by light when free of excess acids) and are hard to settle.
Since you add a very small amount of chlorides (in the water) it will take only a very small amount of your silver out of the solution as the silver halide salt precipitates, which can be allowed time to settle, decanting and filtering the solution to remove any chloride boded to the silver...
The tiny amount of silver chloride is not that much of a problem, although silver chloride's fluffy nature makes it hard to settle and can be somewhat troublesome when filtering in general, you would have much to worry about even if you did not filter that tiny amount out.
Where silver chloride would become more of a problem, is if where you have larger volumes of halogens such as chlorides in with the silver you are planning on melting, where the chlorine or other halide gases formed in the melt will take your silver up into the smoke with them, basically making your silver a volatile gas in the melt, so here the chlorides would have to be either driven off slowly with heat, or the silver salt changed in the form or type of its salt, or the silver salt converted to elemental metal, or flux melted with a reducing agent like sodium carbonate.
With such a low amount of chlorides added here (what was included in some water would not be a problem that I would lose much sleep over, although I would get distilled water, and pay more attention to what I added to what in the lab.