You would need to release the clipboard contents somehow. Avoiding files can be done via a pipeline. For that there exists the xclip utility. It is not installed by default, so unless another program installed it as a dependency you may want to run
sudo apt-get install xclip
Once you install it, you can do
xclip -o sel clip | wc
Note that there exists ...
One solution is 'echo'ing the clipboard content and pass the content to wc:
$ echo -n "your text" | wc
0 2 9
0 newline, 2 word and 9 characters.
As your text is inside your clipboard, you can paste the content in the terminal easily using Ctrl+Shift+v.