Use a vegetable peeler to peel strips along the length of the cucumber, leaving about half an inch of skin between each peel. This gives the slices a fun, striped look while keeping some of that fresh crunch. Then slice the cucumber into 24 thin, even rounds.
Cut the cheddar cheese and deli ham slices into quarters. This makes them the perfect size to fit right on top of the cucumber rounds without hanging over the sides.
Scoop the whipped cream cheese into a piping bag and snip off the end. Pipe a small dollop onto the center of half your cucumber slices (12 of them).
Place a quarter slice of cheddar cheese right on top of the cream cheese. The cream cheese will help hold it in place.
Next, fold each quarter slice of ham in half, and then fold it in half again, so it forms a little layered wedge. Set one folded piece of ham on top of each cheddar slice.
Finish by topping each stack with another cucumber slice, sandwich-style, and secure the whole thing with a toothpick through the center.
Serve them right away for the best crunch, or cover and chill in the fridge until you’re ready to snack or share!