The best way to cut cucumbers into ribbons it to use a mandoline, but a vegetable peeler also quickly and easily does the trick. Trim off the ends, peel the skin and halve the cucumber. Then holding one half firmly on a cutting board, push the vegetable peeler lengthwise away from your body, exerting firm but even pressure. Repeat with the remaining three halves. If you’re in a real rush, simply peel and slice the cucumbers.
In a large bowl, toss the cucumber ribbons with ½ teaspoon salt and ¼ teaspoon pepper. Set aside.
In a large skillet over medium-high heat, heat half the butter and all the oil. Season fish with salt and pepper, to taste. Place fish flesh side down in skillet and sauté until crisp and brown, about 4 minutes. Flip carefully and sauté for an additional 4 minutes, until just cooked through. Keep fish warm. Wipe out skillet with a paper towel.
Heat remaining butter over medium-high heat. Add cucumber to skillet and sauté stirring occasionally, until heated through, about 2 minutes. Stir in vinegar, tarragon and sugar substitute.
Divide cucumber on four individual serving plates; top each with a piece of salmon.