In the discord chat for Death's shadow, the consensus has been a splash in another color is generally considered a tertiary color (e.g BUG death's shadow,) rather than a splash. There are other benefits to running bug, such as access to sylvan library for card advantage and berserk to close out games.

Generally from what I've gathered, the standard green prescence is something like:
1 Sylvan Library
2 Berserk
SB: 3 Abrupt Decay

Going for green does however make your manabase less consistent, so I would consider that when contemplating the additional color.