For a silky smooth result, go all in. Hold the cucumber firmly, and start at the stem end, pressing the peeler against the skin at a slight angle. Pull it down in one long, steady stroke.
How To Peel Cucumber - Foods Guy
Don’t press too hard—let the blade do the work. You want to remove only the dark green layer, not a half-inch of the interior. Thin, translucent strips are the goal.
If you hit a tough spot, rotate the cucumber and start from a fresh angle. Practice makes perfect. Soon, you’ll peel a whole cucumber in under 30 seconds, barely looking.