A formulation of the Skyrme model as an embedded gauge theory with the cons
traint deformed away from the spherical geometry is proposed. The gauge-inv
ariant formulation is obtained by first generalizing the intrinsic geometry
of the model and then converting the constraint to first class through an
iterative Wess-Zumino procedure. The gauge-invariant model is quantized via
the Dirac method for a first-class system. A perturbative calculation prov
ides new free parameters related to the deformation that improve the energy
spectrum obtained in earlier approaches.