For the cookies, in bowl of a stand mixer fitted with the beater attachment, mix flour, lime zest, sugar, and salt on low speed until combined, about 5 seconds. With mixer running on low, add butter 1 piece at a time; continue to mix until mixture looks crumbly and slightly wet, about 1 minute longer.
Add vanilla and cream cheese and mix on low until dough just begins to form large clumps, about 30
Use hands to roll dough into 1-inch balls. Place on parchment-lined baking sheets, spacing about 1 1/2 inches apart. Bake one batch at a time in 375-degree oven until lightly browned, about 12 minutes. Cool to room temperature.
For the glaze, whisk cream cheese and 2 tablespoons lime juice in medium bowl until combined and no lumps remain. Whisk in confectioners' sugar until smooth, adding remaining lime juice as needed until glaze is thin enough to spread easily.
Dip tops of cookies into glaze and scrape away excess, then dip into coconut. Set cookies on parchment-lined baking sheet; let stand until glaze dries and sets. Store in an airtight container for up to four days.
Note-to make the superfine sugar, pulse 3/4 cup of sugar in a food processor for about 30 seconds.