Good and bad news.
Good news was that I was able to remove it, bad news is that I have been able to replicate the problem.
The removal was a strange task. I first replaced the file with the inuse program replacing it with just an text file containing one full-stop. After successive reboots, explorer still maintained a handle to the .exe file. Placing the apm.exe on the desktop with the suspect .exe did not produce the same effect??? So that is pretty suspicious in itself.
Once I discovered that, the removal involved kill the handle off in process explorer and killing from the command prompt (as every time the desktop where the file lived was viewed, it would lock it again). So no real problems there and it proved that explorer.exe was locking it.
The real bad news was that I attempt to repeat the incident. I tried several times to do it, but couldn't find what I did to cause the initial locking to occur.
So sorry for the false alarm, I hope the results have been interesting and mind boggling for you as they have been for me. Thanks for all the help!