Are all track cogs the same width?

I ask this because of a problem I am facing with a recent conversion. The bike was a mid 80s, 27" wheeled, 14 speed. With the rear wheel's freewheel removed there is not enough room to spin on a Dura-Ace cog and a BB lock ring. The cog fits ok, as will a BMX freewheel. Are there cogs that are thinner in width than the Dura-Ace?

This is the second time I've come across this situation.

Adker