Is there any way of mapping ⌘c to ^c

I use Screen Sharing on my Mac to access VNC servers on Linux machines.

This works OK, but I have been using a Mac for years, and ⌘c and ⌘v have become muscle memory. I spend as much time undoing "edits" and deleting c and v before I remember to use ^c etc.

Is there any way of mapping ⌘c to ^c (either in Screen Sharing or in Linux)?