I'd say it follows the rules for assault and heavy weapons. Assault weapons can always fire using full BS, if the bearer moved or not and the bearer can assault after shooting. Heavy weapons can shoot with full BS if the bearer didn't move and with BS1 if he did, but the bearer can never assault after shooting.
The splinter cannon entry says, that it can be fired either as a heavy weapon or as an assault weapon, so I'd say it is our choice.
So yes after moving you can choose to fire 4 shots normal or 6 at BS1.
More interesting are situations, were only snap shots can be fired, like shooting out off a vehicle moving at cruising speed, shooting fliers or overwach, were we always fire snap shots, regardles of weapon type. One would be stupid to fire 4 shots instead of 6.
I must rule with eye and claw — as the hawk among lesser birds.