Changing stylesheet of theme dynamically?

Here is a quick question to wordpress pros:

I have a theme which uses multiple stylesheets. Now i want to show demo to my users. For that i currently use a wordpress plugin and themes can be viewed using https://www.mysite.com/?theme=mytheme and this only shows default stylesheet.

The theme allows changing stylesheets in admin theme options.

Is there some thing i could pass like https://www.mysite.com/?theme=mytheme&style=blue