Religious don't always want a service. My father's wish, before he died was to be cremated and have his ashes scattered over a golf course. He didn't want a service at all. So we didn't give him one. He went straight from the VA nursing home (he was 57) to the funeral parlor and then to be cremated. Came back four days later inside a ziploc bag (yes... he was in a baggie), which was inside a velvet draw string bag, which was inside a small wooden box.
Disclaimer: I am only responsible for what I say, not what you choose to understand.