First, without his assasination, it is likely that Villiers, Duke of Buckingham would have led the second fleet sent to relieve La Rochelle from the siege. I doubt that he would have had more success than in his first attempt, although he may very well have actually fought a battle, rather than retire at the first sign of resistance, as the new leader of the second fleet did.
Beyond the Siege of La Rochelle, I think Buckingham's main significance would be as another cause of tension between King Charles I and Parliament. Parliament had already launched several inquiries into Buckingham's disastrous military expeditions; when those inquiries concluded it is likely they would have demanded that Buckingham be excluded from government. Charles II would either agree to this, or more likely, refuse. An earlier breakdown in Royal-Parliamentary relations could lead to an earlier personal rule of Charles II.
In the event of a civil war, it is possible that Buckingham would hold military commands for the King. Since Buckingham never led a successful military expedition, it is likely that he would have hurt the royal cause with his conduct.