Hi OP, I'm a Celebrant and have led many funerals, cremations, memorials and celebrations of life (and happier ceremonies too of course).
If it helps, try not to think of the Direct Cremation as a 'disposal'. I can assure you that crematorium staff are just as respectful during a Direct Cremation as they are at any other service. They will take good care of the deceased and follow exactly the same rituals - bowing their heads as they approach the coffin, taking a reflective moment before the final moments etc.
I speak to many families following a bereavement and know how devastating it can be. I lost my own mum a few weeks ago. Emotions are understandably raw. As others have said, this method of direct cremation is becoming increasingly popular. Separate this into two distinct parts, with the cremation being one part, and a 'farewell' (wake/celebration of life/memorial etc) being the second part. Much like a wedding, you have two components, one is legal - the registration of the marriage - and then there is the celebratory aspect, which can be done anywhere!
You and your family (and whoever else) can have the second part ANYWHERE at ANY TIME - a Celebration of Life is beautiful. You don't need permission or approval either...and people can come or not, it's up to them. Some of my most memorable services have been just this...many are months after the actual legal cremation has taken place, some are on the same day. But all have been so much more than 'a funeral'.
Please do consider doing this, even if it's only for yourself and a few others who would like to mark the passing of your loved one. You don't need a Celebrant if you don't want one either (although obviously I'm biased) - if you have someone who is confident to lead it, ask them.
At the end of the day though, our own feelings need to be put 'on the shelf' for now and we always need to respect the wishes of the person who has died. We can take ours down off the shelf to explore and work through later.
Take care OP, I know how you must be feeling, and hope that you find your own peace during the coming weeks and months.