Soak 12 wooden skewers in water, 15 minutes. In a shallow dish, whisk together 1 tablespoon each soy sauce and lime juice and 1 teaspoon each sugar and ginger. Add beef, toss, and let sit 10 minutes.
Meanwhile, in a blender, puree remaining 1 tablespoon lime juice, 3/4 teaspoon sugar, and 1 teaspoon ginger with peanut butter and 1/3 cup water. Season with remaining soy sauce.
Heat a grill or grill pan to medium-high. Thread beef onto skewers. Clean and lightly oil hot grill. Grill beef until charred and cooked through, 3 to 4 minutes per side. Toss ramen with peanut-ginger sauce. Serve with beef and cucumber.
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