Zinsser Cover Stain is a great choice of primer/undercoat for Sikkens AZ, it is much better than the dedicated Sikkens Onol Undercoat.
However, if you are changing from black to white you will find one primer and one topcoat won’t offer sufficient opacity. You will definitly need two topcoats, maybe three. If you applied two coats of Cover Stain and one coat of AZ this might work but you would need to try a section first. I wouldn’t try sanding the black colour off if it is adhering well. There is no need, and you will just create more work for yourself.
If you haven’t used either product before I would get a litre of Owatrol Oil to condition the paint. It will help both products flow easier.
A word of warning about Sikkens AZ, it is not an easy product to apply. It doesn’t brush onto the surface well and has a tendancy to build up and run. It can also take an age to dry.
Have you thought about using a water based product instead? Sadolin Superdec Gloss won’t give you the very high shine of the AZ, but would apply in half the time and give good results. Apply this product over the Cover Stain as you would the AZ. This paint will require two topcoats for maximum sheen level. To condition this product I would go for XIM Latex X-Tender available from Decorating Direct.