Multiple Site Designs and Hosting

Hi,
I have several clients that I want to design sites for in WP. My question is can I design them locally or do they have to be msyql hosted? Thing is, some of these clients already have sites up and running and what I am developing for them will replace their current site but that site needs to stay live and uninterrupted until I launch the completed new site. Can I build sites on my computer – iMac Duel Core – like I normally do in Dreamweaver?

Thank you, anyone in advance….

Art 🙂