How to add paprika flavor to mayonnaise without paprika color
My personal method for adding flavor to homemade mayonnaise is to include some flavored oil in addition to the vegetable oil. I like just a touch of chili oil (a teaspoon or so -- too much, and it gets too spicy and/or weirdly red).

Paprika-infused oil can be purchased or made at home (Google search) -- this may meet your needs, or inspire you to try other flavors. (You can also try infused vinegars!)