Back when my kids were babies, we'd keep a box of baby wipes on the kitchen table to use for post-mealtime cleanup. Once the kids got older, the wipes dried up because they just weren't getting used as much.
But we still occasionally have sticky messes (like when the kids drink the melted ice cream out of a bowl of ice cream and manage to get ice cream on their foreheads) that could use some wet wiping. So one day my daughter had sticky fingers after dinner and I had an idea – I spritzed her hands with the water spraying bottle that I keep at the table (for taming my son's hair in the mornings), had her rub her hands together like she was washing them, and then she wiped them off on her cloth napkin. Voila! No more sticky hands!
The kids will even let me spritz their faces to get the ice cream off their foreheads – probably because it's such a novelty for mom to spray them with water at the dinner table. And it doesn't end there! At the end of the meal, I grab one of the dirty napkins and the water spritzer, spritz the sticky mess on the table and wipe clean with the cloth napkin. The napkin goes into the laundry and everything is clean!