Quantitative or qualitative analysis? I would try to extract solvent with another organic solvent (after spray dried powder dissolving in water). The organic and water layers could be simple additionally separated by centrifuge, followed by GC analysis.
Another technique may be the Thermogravimetric Analysis/Mass Spectrometry , without sample dissolving.
The most simple method we use in residual solvent analysis is TGA although inaccuracies can occur due to residual moisture from the atmosphere being detected as well as your solvent. For quantitative analysis we would use gas chromatography either with MS or FID detection. As Andrei mentioned head-space GC is often the best method as you can achieve accurate quantitative information without the need to use further solvents.