Brian Gaff wrote:

I have a CD player with an IEC socket on it and it has no
earth pin at all

That's a C18 inlet, rather than a C14, my AV amp is the same

so maybe it was made for this sort of appliance,

You can use a C13 lead and it won't use the earth pin, but it's designed
for C17 lead.

but it
would be a little bad if that was being used on a normal computer which has
an earth and a metal case if the psu shorted out as I have had more than
one do over the years by having an internal melt down shorting to the case.

The two-core C13 lead is clearly wrong, I've never seen that in any I've
cut open.