Hello There!
Greetings of the day!
We understood from your message that you are using this plugin and instead of ‘Shopping Cart’ icon, you need some other icon/link that redirects the user to the ‘Request Quote’ page and not on checkout page.
If we understood it correctly then it will require additional support so please let us know in case you would like us to implement the same so that I can share with you the required timeline and cost.
Hope this helps!
Thanks and Regards,
Team ProDesigns