Seedless cucumbers often have small seeds; remove them for this recipe. Do not rinse the noodles after cooking; it will make them stick.
Thinly slice celery and carrots diagonally.
Soak noodles in cool water for 1 hour. Cut into 5-inch lengths with kitchen shears. Cook in boiling water until clear, 2 to 3 minutes. Drain (don't rinse). Place in a bowl.
Add celery, carrots, and salt. Toss with tongs for 2 to 3 minutes. Add vinegar and bean paste; toss. When cool, toss in cucumbers and oil. Serve at room temperature.