Combine all of the ingredients for the tartar, and carefully fold together until the mustard and oil is well incorporated, and everything is mixed well. Use a cold cutting board when cutting the salmon, and make sure that the fish stays cold. To make cutting the salmon easier, place it in the freezer for 15-20 minutes so it firms up. This will also help keep it colder while you are prepping it. Reserve in the refrigerator until service. This can be done up to two hours ahead. Season to taste with kosher salt.
In a food processor, combine the lemon juice and egg yolk. Slowly add in the oil while blending, until the mixture achieves a mayonnaise-like consistency. Do not over-mix. Remove the aioli and transfer to a bowl or container. Fold in the lemon zest and season to taste with the kosher salt. This can be refrigerated and used for up to one week.
In a mixing bowl, combine the Wasabi paste and warm water, and whisk until smooth. Add the rice vinegar and slowly whisk in the oil until the vinaigrette is emulsified. Season to taste with kosher salt.
To serve, place about 3 oz (roughly 1/3 of a cup) of tartar onto each plate. Lightly dollop some of the aioli around the tartar (3-4 tsp. should be enough), and drizzle the Wasabi vinaigrette around the tartar. If you wish, you may layer thinly sliced cucumber or tomato under the tartar as a base, and top the dollops of aioli with little pinches of caviar (Japanese Tobiko or Masago caviar is good inexpensive, but a nice contrast in color to the aioli and vinaigrette).