testing different themes without loosing your original content

Currently I am having a problem with my cart display in the theme I am using. I have asked a question about this problem and the solution that you gave me was to change my theme to Storefront and use the WooCommerce cart. I have looked at the Storefront theme a while ago and passed it up because of the header and footer took so much space on the page. I would like to try the theme again but have been hesitant to switch because of all the time that I have spent developing my site in the theme that I am now using.

Is there a way to test a site with my content and tweak it the way I want it without loosing my preferences in case it does not work the way I would like it to? Will that new site be visible to my customers while I am testing it? How can I test it offline with my content?

My site is http://www.saxeeme.com