Sodium dodecyl sulfate (SDS) is a well-known anionic surfactant that forms micelles in various solvents including supercooled sugar-urea melt. Here, we explore the application of contrast variation small-angle X-ray scattering (SAXS) in discerning the structure and interactions of SDS micelles in aqueous solution and in a room-temperature supercooled solvent. The SAXS patterns can be analyzed in terms of a core-shell ellipsoid model. For aqueous SDS micelles, at low volume fractions, the features due to intermicellar interaction, S(q), in the SAXS pattern are poorly resolved because of the prominent contribution from shell scattering. Increasing the electron density of the solvent by the addition of the urea or fructose-urea mixture (at a weight ratio of 6:4) permits the systematic variation of shell scattering without influencing the structure drastically. For a 10% solution of SDS in water, the contribution from the shell can be completely masked by the addition of 40% urea or fructose-urea mixture. The fructose-urea mixture is a preferred additive as it can vary the scattering length density over a wide range and serves as a matrix to form supercooled micelles. The structural parameters of micelles in supercooled fructose-urea melt are obtained from contrast variation SAXS, small-angle neutron scattering, and high-resolution transmission electron microscopy.