How to prepare floors without a grinder

I want decorative concrete in our basement, but my wife refuses to allow anyone to use a grinder in her house. She is afraid of dust and cancer and all that. She says the cats are too sensitive for even fine dust.

Is there a proper way to prepare the floor without grinding it first?

 

Get rid of the wife and cats for the day!

 

Most grinders have a vac system as well so hardly any dust.