Is there a way setup and test Cowlendar without interfering with Live site?

Yes there is.

What you need to do is duplicate your theme or use another theme which Is draft. To do so click on your theme, then click on the three little dots then click on "DUPLICATE".

When you've duplicated your theme, click on Customize

Then enable Cowlendar on this draft theme and hit save

Once it's done, don't search for the product linked to Cowlendar on the theme editor.

Leave this page and hit "preview" on the duplicated theme. Search for the product there.