Yes, you have a couple of different options.
You can set up flat rates instead of live carrier rates in Shopify, so that on the customer side they're seeing shipping prices that you input manually in your client's Shopify settings. On the fulfillment side, you'd then deal with the carriers directly. The challenge with this is making sure that your custom rates in Shopify align with what your client is paying at fulfillment, and there are limitations on how you can set this up in Shopify.
Alternatively, if it's feasible, you can look at using a third-party solution like Intuitive Shipping. We have integrations with more live rate carriers than Shopify (see the full list here). With Intuitive Shipping, you can connect to one of these live rate carriers -- or you can set up a custom table of rates based on your client's costs, similar to how I described above. However, with Intuitive Shipping, you have a lot more flexibility. You can base the rate table on different criteria like distance, weight and volume, and you can use our Condition system to establish any rules or restrictions that impact your client's shipping strategy. If you'd like to learn more about how to do this, please feel free to book an appointment for a demo with one of our team members.
As Ron have mentioned, one of the ways to go would be to set up flat rates instead of live carrier rates in Shopify. By doing so, the customers will see the shipping prices that you input manually in the Shopify shipping settings. On the other side, you can directly deal with the carriers.
If you are open to use an app, you can check out our Multi Carrier Shipping Label app that would help you integrate with many more carriers than the default Shopify carriers. With the app, you can connect with different carriers and display the shipping rates from these carriers at checkout (provided carrier-calculated shipping is enabled in your Shopify store). Apart from these, you can also set up rates based on different conditions like total weight, a particular weight-range, zones, order quantity, and many more.