Hey there @VincentCavret!
Don here from Shopify.
Thanks for checking in here on our Community forums with your theme editing query.
As the Prestige theme is a third-party theme (ie not a free Shopify one) we're limited in how we can provide support for themes like this here.
Should they not be able to support the specific customisation you wish to make, you could consider hiring a Shopify Expert for some custom coding help (depending on the scale of the project you wish to have done).
We also have a number of merchants and partners in the community here who have experience in changes like this that may be willing to help out directly!
Are you interested in removing the cart icon for more aesthetic reasons or is there a business requirement you feel this fulfills?
All the best!