Worth noting that this is Ctrl+Shift+v and Ctrl+Shift+c.
The C-v (Ctrl+lowercase v) is important for literal character insertion. (Insert a tab, escape, return, etc.)
> The C-v (Ctrl+lowercase v) is important for literal character insertion.
You can remap it to <C-l> (L = literal), and then use <C-c> and <C-v> without shift:
inoremap <C-l> <C-v>
imap <C-v> <C-r>+
cmap <C-v> <C-r>+
xmap <C-c> "+y
imap <C-V> <C-R>+
vmap <C-C> y
Most probably you want this as well:
cmap <C-V> <C-R>+