Using the information provided, the reply comes from State specialist in entomology also having a very strong background in wildlife as the two are often connected. "If the droppings resemble those of a mouse, that is probably what is causing them. Insect droppings, particularly those of the small insects associated with kitchens, are much smaller than those of mice.
Silverfish do not damage books published after the 1950’s because hide glue was substituted for the flour paste used earlier. The silverfish were attracted to the starch in the flour paste. I have never heard of silverfish damaging handles. Their mouthparts are too weak to chew most plastics, and there is no food value there for them.
Mice and other rodents will chew on handles to obtain the salt from perspiration on them. Generally, this is not a problem because the handles of kitchen utensils are washed after use along with the functional end. However, if this person just washes the end that touches food and not the handle, then salt will build up on it. This could explain why they were not chewed after being thoroughly washed, but them chewed after the utensils were probably used. I was taught to wash the entire utensil, but I have seen numerous other people not wash the handles.
Mice are creatures of habit. If they have found a food source elsewhere, they are unlikely to explore other areas looking for food. They may be feeding on birdseed, dry dog food, or other food and are not searching for food in the kitchen."
I will add that our mild weather has allowed mice to move freely, coming and going from our homes. Mice can move through openings under 1/2 inch. Caulking or sealing the openings in the sink cabinet where the plumbing pipes enter can physically keep them out.