Annsixty, this is what we did for my husband too. We did use a sympathetic funeral director to organise what they call a "direct cremation" for us: the body was collected from the hospice and the FD kept it until they could arrange a cremation. No one attended except the FD team, who did this respectfully and asked for a piece of music to play while it was carried out.
Then a couple of weeks later we had a memorial service in the village hall, with the ashes displayed (in a mini beer-keg!). We had a serious bit with readings, tributes and music, then rearranged the furniture and had refreshments. This was what my husband asked for: minimal formality for the funeral, but plenty to eat and drink. Six months later, the family quietly scattered the ashes.
So yes, we did use a funeral director, but their work was all behind the scenes, as we (the family) ran the service ourselves. I should think anyone who says "No undertakers!" means that they don't want an official presence at any ceremony, but no one expects friends and family to do the heavy lifting. Funeral directors have suitable vehicles, strong men, and links with the local crem, so they are best placed to do the actual cremation.
This sort of arrangement is becoming more popular now, and it also saves money - ours was about £1000 less than a full funeral service, which meant we could afford a good party afterwards!