Without some means to compensate for the different spacing and cable pull ratio between Shimano and Campagnolo 10-speed systems, it's not gonna work too well. But the
Jtek Shiftmate exists for just such a purpose, and they make different models for different drivetrain component combinations. For Campagnolo 10-speed shifters, Shimano 10-speed cassette, and a Shimano derailleur as you described above, you'd need a Shiftmate model 3.