This article might help. It's interesting, anyway. Check out the Hubbub Shimano modification.
If I read this right, your Campy 10s cassette has a pitch of 4.15 mm and the Campy 10c Ergo levers move the cable 2.8 mm for each click. The Campy 10s derailleur has a shift ratio of 1.5 and the Shimano rear Dearilleur has a shift ratio of 1.7. The Hubbub modification will reduce the Shimano shift ratio to 1.6. That might be close enough.
Which shift mate do you have. You might be able to swap the pulley.