Can you have a child with the physical characteristics of edwards syndrome but not have any chromosomal abnormalities?

Yes. Some of the physical signs of edwards syndrome are non-specific, that is, shared by other syndromes, with or without chromosomal abnormalities. No one sign is diagnostic, and several signs could be present in a child with normal chromosomes and without its having edwards syndrome.
Genetics consult. Talk to genetics, the child may need in depth assessment by them for additional chromosomal testings or other inhereted diseases.