Hi Mr. Peptide,
I wouldn't worry about the azido group as the conditions you intend to employ are comparatively mild. It isn't uncommon to hydrolyse Evans-type oxazolidinone auxiliary using LiOH in presence of an alkylazide.1,2 The azido group remains stable under these relatively forcing conditions.
1. Evans, D. A. and Britton, T. C. J. Am. Chem. Soc. 1987, 109, 6881–6883
2. Evans, D. A.; Ellman, J. A.; Dorow, R. L. Tetrahedron Lett. 1987, 28, 1123–1126