Results on the study of in situ removal of the glass on the magnetic switching in amorphous glass-coated microwires with positive and nearly zero magnetostriction are reported. A new experimental setup was designed to allow simultaneous recording of the hysteresis loop and domain-wall velocity. It has been found that the wires with positive magnetostriction preserve their bistable magnetic behavior during glass removal and even after. For the wires with nearly zero magnetostriction, the bistable magnetic behavior appears during glass removal at a glass thickness dependent on the wire diameter and is present for further glass thinning. The values of the switching field are decreasing for positive and increasing for nearly zero magnetostrictive wires during glass removal. Both types of wire show a wide maximum in the domain-wall velocity to glass thickness characteristics. The results are explained by considering the complex domain structure of the microwire induced by the balance between the magnetoelastic and magnetostatic energy.