How to change the default shortcuts for copy/paste in urxvt?

Contrary to Thomas' answer, it looks like you can. In the same question he referenced Spencer and Enno both mention that you can bind the native eval extensions in your .Xresources file. This would look like the following:

URxvt.keysym.Shift-Control-V: eval:paste_clipboard
URxvt.keysym.Shift-Control-C: eval:selection_to_clipboard

To disable the previous keybindings, you'll also need:

URxvt.keysym.Control-Meta-c: builtin-string:
URxvt.keysym.Control-Meta-v: builtin-string:

You can reload the file with:

xrdb -load .Xresources

You'll need to restart rxvt for the changes to take effect.