Assuming I start with a known 99.8% purity of isopropanol, after recovery with a distillation apparatus, could I use a hydrometer to test for water content? If so, is there a special one I should use?
There is an image of a table provided by Chu and Thompson  listing isopropanol water solution densities:
The essential data part is (weight % vs density):
There is density gradient -0.0026 / 1 w%, resp. -0.00052 / 0.2 w%, determining purity by density via hydrometers is rather illusory.
Some success could be gained by pycnometers — using special glass flasks with a glass cap with a hollow. You would weight the flask, the flask with water and the flask with isopropanol and you would calculate the density.
In any case, as differences are minimal and as liquids have considerable thermal dilation, one must carefully watch the liquid temperature.
In case of the pycnometry measurements, the glass and both liquids must have the same temperature, the best the one for which density is tabelized.
- Chu, K.-Y.; Thompson, A. R. Densities and Refractive Indices of Alcohol-Water Solutions of n-Propyl, Isopropyl, and Methyl Alcohols. J. Chem. Eng. Data 1962, 7 (3), 358–360. https://doi.org/10.1021/je60014a011.