Is it morally correct to feint sadness for the sake of others?

Strange question I know. I have recently had notice of a loved one who has died and have to go to a funeral but after decades of practising the dharma my mind is unmoved by such things, where my peers are non buddhist puthujjana so are of course going to be swept up in the usual swirl of emotions after a loved one has died. My question is, is it morally correct to fake sadness to fit in with others as how they would assume a person would/should react. As a Buddhist, its just another day in the life of samsara. Sure I have compassion for people who have lost a loved one and are feeling suffering but to me the whole deal is rather trivial. Death is just a part of the cycle. Does not help that I am from a traditional christian country, where the funeral will also be a christian service and death here is seen as an innately sad thing. It is usual for funerals to be very sombre and quite depressing.