Campagnolo single speed conversion - can I use a 10sp cog? I have a set of Miche reflex wheels.
I would like to use them for a single speed conversion project on a Peugeot frame.

can I use a 10sp cog?
what I mean is:
can I use one of the normal cogs that are on one of my 10 speed campag cassette to do it?

This would allow me to use all the gear that I have like:
 - 10 speed chain (after being shortened)
 - original 10 speed chainring
 - one of the 10 speed cogs
Yes this is possible with a free-hub style hub, but you may run into some issues.

You can use a sprocket from a 10 speed cassette, and replace the other sprockets with spacers. You can place the sprocket in the spacer stack to achieve good chain alignment. 

I don't know how Campagnalo cassettes are built but Shimano cassettes combine the largest sprockets onto a spider, so you would not be able to use those individually.

Cassette sprockets are of course designed to enable the chain to come of them easily when shifting, so they are not as good as retaining the chain as a purpose made single-speed sprocket. For the same reason you may have an issue with the chain coming off the chainring without a front derailleur. This is why 1x systems use a 'double-wide' chainring for better chain retention.

Sheldon Brown has a page that deals with single speeds: https://www.sheldonbrown.com/singlespeed.html, find the section titled 'Cassette Hubs'.