Hello,
Ok I process some tests to try to understand what's going on, and I think I have a theory, I will guide you to process a test, follow me step by step :
1. Go to your Cart Design plugin folder :
=> YourWebsite\plugins\hikashop\cart_design
2. Open the file cart_design_view file :
=> Go around line 9, see my screenshot
You will have this code :
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.0.10/css/all.css" integrity="sha384-+d0P83n9kaQMCwj8F4RJB66tzIwOKmrdb46+porD/OvrJ+37WqIM7UoBtwHO6Nlg" crossorigin="anonymous">
Can you add these code elements "<!--" & "-->" in order to comment this line to have finally this :
<!--
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.0.10/css/all.css" integrity="sha384-+d0P83n9kaQMCwj8F4RJB66tzIwOKmrdb46+porD/OvrJ+37WqIM7UoBtwHO6Nlg" crossorigin="anonymous">
-->
And process a new test with the Design cart
published to see if that solve your issue.
Awaiting your returns to progress on your subject.
Regards