Preparing previously tiled cement floor for vinyl tiles

Hi folks,
We are getting rid of all tiles in the house so we don't have any grout to clean (and there is plenty of mold in this semi tropical coastal region).
The last job is the toilet floor. It has those small 2cm square tiles. We were told the tilers could just float a surface over them and lay the tiles no trouble - but - the neoprene they use costs a fortune, the tilers have to come out 3 days in a row to put on a new coat each day - and as we are 25km out of town guess who pays for travelling time.

Suggestion now is that I remove the tiles, scrape on a thin finishing layer, and the tilers will do the rest - saving a small fortune.

I can remove the tiles OK - with a lot of cold chisel work - they are well fixed on - but how do I get the cement underneath as near to perfectly smooth as possible - any bumps or grit will show through the vinyl tiles.

Thanks
Don

Wouldn't it be a lot easier to pull up the cement sheet as well and replace with new sheeting ?

Sounds like a good idea, except the cement sheet was laid first and the walls built on top of it. Then a layer of cement - I was hoping to avoid removing the layer of cement as it would need a jackhammer to remove, even then it would not all come up as the cement was laid directly on the cement sheeting, on layer of plastic, etc to make removal easier. (I watched the builder trying to remove the cement floor in the bathroom when it was renovated).
Don