Hot iridised finishes are quite hard and emulsion or acrylic paints are unlikely to bond to the finish, not sure about solvent based paints though.
Cold applied iridescent finishes are not bonded to the glass and can flake even with normal handling and also due to airborne pollutants.
Professional restorers of paintings do have to face the challenge of removing paint from fragile surfaces and they do this using good quality scalpels and powerful magnification slicing the paint be removed in the tiniest chips to minimise mechanical stress. They will also use solvents where possible.
This approach should make it possible to restore the most fragile surface and I would try and use that if I felt there was any risk, first testing durability of the iridising under the base or other out of site position. Scraping on an iridised surface will always have a risk so better to work as slowly as possible. A final option would be to repair not restore, by simply colouring the spots to blend in with the surface - suitable paints exist in the better art shops.