The answer is no because cats aren’t self-conscious (self-aware), period. I could leave it there because anything else is strictly unnecessary.
However, the question is really on the topic of whether cats feel embarrassed by a lion cut. And once again the answer is no. Embarrassment relies on the ability to be self-aware. You have to know that you exist and be able to observe yourself and comment on yourself.
It is pretty well universally agreed that cats can’t do this. I have read a lot about this from excellent cat ‘experts’ with backgrounds in zoology and other sciences. Currently the evidence is not there to allow us to say that cats are self-aware and therefore able to feel embarrassed when given a lion cut.
De Gustafson gave her Persian cat, Bob, a lion cut because she lives in Florida and it is very hot. That is fair enough.
After the cut the other family cat understandably no longer recognised him and hissed at him. I think this hostile reaction from a formerly friendly cat was mainly because Bob smelled of perfume for some reason. Perhaps the groomer has dusted him with talcum powder or something.
When friendly cats can no longer recognise their buddies because their body scent has changed significantly they treat them as strangers and hiss at them. It is about scent not sight (visual appearance).
But this would not make Bob embarrassed and self-conscious. Although De Gustafson believed that Bob was made self-conscious by the attentions of his feline mate and the family dog who licked Bob. I am afraid she is wrong.