I suspect there's no firm answer to this, but I'd be interested in opinions especially if there are some hints in the various extra Sandman books (I've only read the 75 comics).
Daniel says the person responsible for Despair's death will be in agony for the rest of time and that fits with Loki being bound under the serpent. It also seems in character for Loki, especially if Daniel's statement indicates Loki devised the murder but didn't actually do it himself. Having said this, I guess it would have been mentioned at some point if Loki was responsible.