Strain court bouillon, reserving solids. Transfer solids to a large fish poacher and set over two burners on the stove. Insert rack and lay salmon on rack. Trim the tail if necessary to fit inside. Add cooled court bouillon to cover the fish completely; or if only a small bit of fish is showing, you can cover it with a piece of parchment paper, cut to fit inside poacher.
Bring the liquid to a simmer over medium-high heat, then immediately reduce heat to medium-low. Check temperature with a candy thermometer and adjust heat so it is between 160 and 180 degrees. Very few bubbles will break the surface but there should be steam coming from the surface. Poach salmon, covered, adjusting heat as necessary to maintain the proper temperature, until an instant-read thermometer inserted into the thickest section registers 130 degrees. Fish will continue cooking off heat. You can also test by inserting a knife into the flesh along the backbone; the flesh should still be slightly translucent and offer little resistance. The cooking time should be about 5 minutes per inch of thickness once liquid has reached a simmer, about 30 minutes. Remove poacher from heat and allow it to cool until you no longer see any steam, about 1 hour. Lift the rack with the salmon from the poacher and set it over a large pan or the sink to allow the salmon to drain until just cool enough to handle, about 30 minutes.
Transfer salmon to a clean work surface. Use your fingers a paring knife to pull and scrape off the skin from the top side of the fish. Use the back of the knife to scrape off any brown areas from the surface. Using two large spatulas carefully slide the salmon onto a serving platter. At this point, the salmon can be covered with plastic wrap and refrigerated for up to 4 hours.
Slice the cucumber lengthwise into very thin strips. Arrange the strips diagonally across salmon, spacing them about 1 inch apart, and tuck the ends underneath so they appear to wrap around the fish. Garnish with watercress. Separate into pieces and serve sauce and lemon wedges on the side.