Can I make it so user can change theme colour scheme in 1 click at the front of site?

This is probably the most random question you have ever heard as it certainly is mine !

My client is asking me to create a website in blue and have a duplicate website exactly the same in green, linking to each other. I was wondering if I could create a link (in a widget or something) to the 'green' site and the 'blue' site, but linking it to the same url and only changing the colour scheme?

It sounds like it could be plausible, however I have no idea to do this so any help at all would be appreciated I have just started to study php, MySQL and JavaScript but am nowhere near good enough to figure this one out.. anyone have any ideas?

Thank you ever so much!!!