This is simple, you don't actually need to share the C drive but only reinstall the File and Print sharing service on the Hyper-V virtual network card.
Also if you’re facing any problem or restrictions on your network profiles, consider changing the default "unidentified network" for the "vEthernet (DockerNAT)" card to private via this PowerShell command.
Set-NetConnectionProfile -interfacealias "vEthernet (DockerNAT)" -NetworkCategory Private