Hello Chris,
From your question, I suppose you simply want to bypass the booking system and use your other platform where you have your own system. To do that, simply go to Appearance >> Customoize >> Woocommerce >> Book Now Button Settings and enter the URL where you want the users to proceed to / or where you have your own Booking system. You can also change the “BOOK NOW” button label from there to any other specific label you require.
Alternatively, you can also use WC’s Catalogue Visibility Options plugin (third party premium plugin) which lets you replace prices and book now buttons in a way to make the site an online catalogue and remove its commerce functionality.
Removing WooCommerce will cause the issue mentioned because we have integrated the theme to utilize WC for creation of products / categories etc. So that is not recommended.
Thank you