FWIW, Several CZs I have that are CZ 'custom' guns have no serial number on the upper or barrel (Accu-Shadow and CTS LS-B .40)
I'd personally go for the option where you have them grind the serial # off and re-polycoat, then you have a nice shadow upper for this gun or anything else laster w/o worry. Then if it tests/groups well, you are golden.
BTW, I think you are a little lucky to get a Shadow, especially if it is a sub $1000 non-custom one since you are talking about potential custom work. If you notice, CZ-USA no longer lists the non-custom shadows as a catalog item, so I think the only way to get these is if something still floating around un-sold - I don't know if AA or CZC still selling these or if the way demand is all of them are shipping as custom or Accu models now?