Technically, a funeral is not obligatory, but it is highly encouraged. Not only does it provide powerful prayers (nothing greater than Holy Mass), but it helps the grieving to move through the loss.
If the interaction between estranged family members is the primary driver of your fears, let it go. It can be done discretely. If you so desire, talk to the funeral director in advance about that because they handle obituaries and public information.
As far as being alone, your son would not be alone, if the funeral were done in a parish that merges it into the daily Mass, as mine does; so there is always a contingent of praying, compassionate people.
So have a few discussions with the relevant people, especially your son, so that his wishes are honored too. Keep in mind, God can work great healing for the bereaved through this Christian rite; don't sell it short before you have worked this through.