Yes, you can omit the words "that of" in this situation but it sounds slightly less sophisticated if you do.

"like that of" is a comparative. In your example - It is detailing/comparing the ceremony to a funeral. Another example: My pet's body size is like that of a rabbit.

At first I did not understand what you meant, but after I changed a couple of words I understand it now. "of that" is not the right words and should should be left out, but to make it sound better you have to change some other words. I would write "American Wake" means a ceremony LIKE a funeral FOR someone going to America, because you will never see THEM again. Here 'them' would be better than 'him or her' I would also use 'a' for ceremony because it is said in general not specific terms