Campy 10-speed cassette cogs are spaced slightly wider than Shimano's and a 9-speed Shimano chain does work well with them. When Campy first introduced 10-speed and it's very problematic chain, many riders reported using Shimano 9-speed chains with good results to avoid the Campy chain.

BTW. I'm surprised your shifters won't cover the full cassette range. Try shifting into the smallest cog, disconnect the shift cable at the rear derailleur and pull ALL the slack from the cable. Tighten the clamp bolt and that should do it. Otherwise be sure your low limit screw isn't set too tight as that will also prevent reaching the largest cog.