The simplest method I can think of would be to download all four required packages to upgrade the kernel. Save them to USB (either the same one with Zorin on it or a separate one). Install Zorin, then once the installation is complete, reboot. Upon opening the desktop, immediately install the later version kernel you downloaded and saved to USB earlier.
If you save it to the same USB Zorin is on, just reboot, plug in the USB and mount it to Browse the files, then install them using the terminal.
Open the terminal in the directory your .deb kernel packages are in.
Use sudo dpkg -i <PACKAGE-NAME>.deb to install each. If you get a dependency on one of the other kernel packages, just install that other one first.
This way you avoid trying to replace the kernel call in the ISO you burned and also avoid needing to use WiFi or LAN right at the outset and can get the kernels installed quickly.
Then reboot and test.
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