There is a solution mentioned in Wikia:
function! Putclip(type, ...) range
let sel_save = &selection
let &selection = "inclusive"
let reg_save = @@
if a:type == 'n'
silent exe a:firstline . "," . a:lastline . "y"
elseif a:type == 'c'
silent exe a:1 . "," . a:2 . "y"
silent exe "normal! `<" . a:type . "`>y"
call writefile(split(@@,"\n"), '/dev/clipboard')
let &selection = sel_save
let @@ = reg_save
vnoremap <silent> <leader>y :call Putclip(visualmode(), 1)<CR>
nnoremap <silent> <leader>y :call Putclip('n', 1)<CR>
just copy these lines to .vimrc and your \y will do the trick, whether you are using vim or your mouse to select texts.
This may not be a problem since you already have access to the clipboard, but /dev/clipboard is available for Cygwin version 1.7.13 and higher.