My mum loathed funerals. She was a very private person and felt that funerals were a chance for people to turn up and parade their grief, even if they hadn't seen the deceased for years or didn't have a profound relationship with them. When my dad died, she chose not to have a funeral for him - the undertakers handled the cremation and, at the time we knew it was taking place, the immediate family gathered together at her house and shared our grief in silence.
When mum herself died, she said in her will that my sister and I could decide whether or not to arrange a funeral, and that we didn't have to feel under any obligation to attend. In the end, my sister felt that a small funeral would give us closure. Again, it was just immediate family and we did everything ourselves, i.e. the music, the reading, etc. It was good because it felt personal to us.
I don't think anyone should feel obliged to hold a funeral if they don't want to. Similarly, if you don't want a funeral yourself, you should tell your family and they should respect your wishes.