We have looked in all of the reference books that would be likely to have input on this question, and asked a number of pretty well informed people and haven’t come up with a single argument for keeping a silver-plated spoon out of your whipped cream. It would be nice to have a reference book about old wives’ cooking tales, too, but we don’t know of one.
At the same time, it’s not like whipped cream needs much of an excuse to go flat, especially in hot summer weather. At its best, it is an insubstantial suspension of air, water, and fat droplets, where the air wants to escape, the water wants to collapse, and the fat is just looking for an excuse to turn to butter. You will always find it easier to whip cream if you chill the bowl and whisk or beaters as well as the cream before you begin to whip. And if the air in your kitchen is hot, you may need to whip the cream over a bowl of ice, or in many cases, the hot kitchen air will simply keep the cream from whipping.
If your whipped cream gets hot, the fat droplets that hold the structure together melt. And, we suppose, if a silver- or gold-plated or even, tsk!, stainless-steel spoon were to conduct a little extra heat to your bowl of already sagging whipped cream on a hot day, you would probably have the teensiest justification for blaming the spoon, at least partially.
But then someone might accuse you of being an old wife, and nobody wants that….