You could write a mapping in the .vimrc, but I don't know if that is what you should. Do you only want to map the c command, or the behavior of all copy/paste commands. Because a normal installation of Vim will not use the clipboard and you most likely have a setting in the .vimrc that tells Vim to use the clipboard at default. Normally the unnamed register "" (which is " the unnamed one) will be used.

What about an alternative c command, without changing the normal behavior? In example this mapping in .vimrc:

nnoremap <leader>x "ac
nnoremap <leader>c "ay
nnoremap <leader>v "ap

The default leader-key is backslash. Now in Normal mode when you type \xw it will cut the word into register a. \v will paste from register a. You can remap the leader key to something else, in example the spacebar (like I do).

" Leader key space
let mapleader=" "
" Make sure spacebar does not have any mapping beforehand.
nnoremap <silent> <space> <nop>

I don't recommend to change the default behaviour of c, that is why I recommend to use it with leader key.