My DD is an Independent Celebrant who on average conducts 3 funerals a week. The format is entirely the 'customers' choice, be that the bereaved or the 'deceased' themselves. DD has met with several people who knowing their time was short have planned their own funeral right down to the music, flowers and what is to be said. Funerals vary from the very formal, traditional, through forest, ashes at sea, etc to very informal or non-funerals. Locally, the nearest crematorium is nearly an hour away and many people do not want to subject mourners to this journey so sometimes there is a short ceremony in a funeral parlour or local hall or hotel, perhaps followed by a lunch or funeral tea, while the undertakers take the coffin to the crematorium themselves or perhaps accompanied by a couple of mourners or just the celebrant.
Sometimes the timing is reversed there is a cremation with no ceremony in the morning followed by the service in the afternoon.
There is a legal (Public Health) requirement that a body is either buried or cremated but no stipulation that there has to be any ceremony. Undertakers will treat the deceased with dignity and respect even if no one else is present. Quite a few people opt for no ceremony on the cremation or burial day and have a memorial dinner or service/ceremony at a later date, some have a scattering of ashes or a wee ceremony when ashes are buried in a family grave. I know one family, from all corners of the UK, who meet each year and climb the hill where their loved ones ashes are scattered.
Personally, I think a scattering of ashes, on a nice day in a lovely place or at the seaside would be far less traumatic, especially for children than travelling miles to an impersonal crematorium or standing at a graveside in the pouring rain.