Cavani has 17 goals in 36 CL games. That 0.47 ratio is on par with the likes of Agüero, Henry, Shevchenko, Del Piero and Drogba, among others, and better than many more. So it's a bit of a disservice to say he wouldn't score goals for us in the competition. His EL record makes his continental record even better.
Of course Morata really excels in the competition because his attributes as a quick counter attacking striker really suit it. So far in his career he's averaging a CL goal every 180 minutes, Cavani is basically the same, but of course Morata has growth potential.