I've come across he shams sick
Can I say he shams an idiot or he shams pain in his back ? Do I have to use a person or a thing after sham?
I know it's a rare word but nevertheless
You should be able to substitute the verb feigns for any transitive use of shams.
So He shams idiocy. rather than He shams an idiot.
IMO, He shams sick would be better as He shams illness because sick is not an appropriate object.