Melt butter in a large skillet over medium-high heat; add shallots, and sauté until tender. Add chard and mushrooms, and sauté 6 minutes. Stir in whipping cream, next 4 ingredients, 1 teaspoon salt, and 1/2 teaspoon pepper. Set aside.
Trim fins from back, belly, and near gills of salmon with kitchen shears or a sharp knife. Rinse cavity, and stuff with chard mixture. Sprinkle fish with remaining 1 teaspoon salt and 1/2 teaspoon pepper.
Cut a double thickness of cheesecloth 17 inches wide and 8 inches longer than fish. Place salmon lengthwise on cheesecloth; top with lemon slices. Wrap cheesecloth around fish; secure at regular intervals with kitchen twine, tie ends of cheesecloth with twine.
Rinse fennel thoroughly. Trim and discard bulb bases. Trim tops from bulbs, reserving bulb and tops. Cut each bulb into 3 lengthwise slices. Place fennel tops and bulbs in a fish poacher or large roasting pan, if desired. Add wine to pan. Place fish on a rack in pan.
Bake at 400° for 45 minutes or until a thermometer inserted in thickest portion of fish registers 135°. Let cool 15 minutes.
Cut and remove twine; slit cheesecloth, and fold back. Remove fish head and tail, if desired. Keeping cheesecloth under fish, turn fish over carefully, so rack side faces up. Peel skin off using a paring knife. Holding cheesecloth, invert fish onto a serving platter, skin-side up. Peel off remaining skin, scrape away any brown fat. Garnish, if desired.
Note: Turning fish twice to skin, as above, gives the prettiest presentation.