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Melt the butter, and combine with eggs, egg yolks, granulated sugar, salt, extracts, vinegar, rum, and sour cream in a large, heavy mixer. Using the paddle attachment, beat on medium-high until lemon-colored. Add citrus rinds. Gradually add enough flour to produce a fairly stiff dough. Turn out onto a floured board, and knead for 8 to 10 minutes, adding flour if necessary, until the dough blisters, becomes elastic, and can be handled easily. Cut the dough in half, and wrap one half with plastic wrap; reserve at room temperature.
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Roll 1/2 of dough very, very thin and cut into strips about 4 inches long and 1 1/4 inches wide. Cut the ends on a diagonal. Slit each piece in the center, and pull one end through the slit. Place on a parchment-lined baking sheet, and cover with a towel to keep moist. Repeat with other half of dough.
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Heat the shortening in a cast-iron frying pan to 375 degrees, and fry the dough strips, a few at a time, for about 1 minute, until lightly browned, turning once with a long fork or tongs.
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Drain chrusciki on brown paper bags; transfer to a cooling rack and sprinkle with confectioners' sugar. Store, tightly covered, in wax-paper-lined tins.