Cook the sushi rice according to the packet instructions.
Mix together the vinegar and sugar in a bowl and stir until the sugar dissolves. Once the rice is cooked, and when it is still warm, mix in enough of the vinegar and sugar mixture to coat the rice grains, but do not allow the rice to become wet. Tip the rice on to a tray to cool quickly.
Take 1 nori sheet and place it on a bamboo mat with the longest side in line with your body and the ridged surface facing upwards. With damp hands, cover three-quarters of the nori sheet with a thin layer of rice, leaving a band of nori at the top without rice.
Spread a little wasabi paste with your finger on top of the rice in a thin line, at the edge nearest to you. Then place a cucumber strip and some smoked salmon on the wasabi.
Use the bamboo mat to start rolling the nori up, tucking in the cucumber and salmon as you go. Once you have rolled up the majority of the nori, wet your finger and dampen the plain edge of nori. Finish rolling up the nori. The wet edge will stick the roll together. Repeat with the other nori sheet. Then, using a sharp knife, cut the rolls into 8 even pieces or 4 even pieces and 1 slightly larger piece cut into 2 on the diagonal.
Mix the remaining wasabi and soy sauce and serve with the pickled ginger alongside the nori rolls.