Combine oil, lemon juice, paprika and sugar in a large bowl, season with salt and pepper and whisk until well combined. Add the mushrooms and stir to coat all the mushrooms. Cover and refrigerate for 1 hour to marinate.
Cut each chorizo into 8 slices. Cut capsicums into pieces. Thread the chorizo, capsicum and mushrooms alternately onto 8 skewers.
Heat a lightly greased barbecue plate on medium-high. Barbecue the skewers, turning often, for 6-8 minutes or until mushrooms and chorizo are warmed through. Serve with salad and lemon wedges.