Baggs
I think since your son had a long-term partner, then it is first up to her what form, if any, a funeral takes.
This may sound harsh but hear my story first. My daughter died earlier this year. She had a long-term partner and they had two kids. DD did not want a funeral and made this known to her life partner. He in turn made it known to DD's relations and to his own side of the family. He expressed his wish to honour his life partner's preference.
We all went along with that.
In my case, as it happens, going along with that actually meant being extremely relieved. I had been dreading the funeral from the moment we knew of her terminal diagnosis. My son-out-law arranged a private cremation.
The he and their kids did a very special thing with the ashes in a very special place to DD. We all know exactly where it is and some of us will go there and visit that place when we can.
I don't think it would be unreasonable for you to make your preference known but in your position I would wait until you hear what your son's partner wants.
I wish you well in your grief and send heartfelt condolences.
Awful to have a child die, however old they are, whatever the circumstances.
You sound as if you dealt with it all very sensitively 