The first thing that should be said is that the primary sources for the kings of the West Saxons in the first half of the seventh century are at best sketchy. Cwichelm may not even have been the king of the West Saxons but it is probably safe to say that he was at least 'a' king of the West Saxons - and specifically those that were located around the Upper Thames valley.
At the time that Cwichelm features in Bede's Ecclesiastical History of Britain, in the year 626, the West Saxon regnal list - such as it is - shows Cynegils as King of Wessex, but then also shows that a son of his was called Cwichelm and that he was supposed to have died in around 636.
The Anglo-Saxon Chronicle has a number of references for Cwichelm, which serve only to complicate things further:
593 - Here Ceawlin and Cwichelm and Crida perished.
611 - Here Cynegils succeeded to the kingdom in Wessex and held it 31 years
614 - Here Cynegils and Cwichelm fought on Bea's Mount and killed 2,065 Welsh
626 - Eomer came from Cwichelm, king of the West Saxons (more of this later)
628 - Here Cynegils and Cwichelm fought against Penda at Cirencester and came to an agreement
636 - Here Cwichelm was baptised in Dorchester and passed away the same year.
I tend to favour the view of DP Kirby that names such as Cynegils and Cwichelm were relatively common and thus it may be the fault of later historians who have tried to conflate several references over a wide period of time to the same person.
Anyway, back to the story of 'King' Cwichelm's unwitting part in Edwin's conversion to Christianity. At this time, Edwin was the most powerful ruler in the Heptarchy, described by Bede as the fifth Bretwalda "who ruled all the peoples of Britain, both Angles and Britons with the exception of the Kentish folk." It was this dominance that most probably resulted in Cwichelm's decision to send an assassin to Edwin's court in 626. Edwin had no doubt been looking to extend his influence to the south where he must have come up against Cwichelm's land. The West Saxon ruler was not about to give in easily to this foreign upstart.
That said, he knew that Edwin was the most powerful king in the island and that direct confrontation would most likely not result in a favourable outcome for him. Therefore he chose a more refined, but thoroughly underhand method of being rid of the Northumbrian king. As Bede says "an assassin named Eumer was sent into the province by Cwichelm, king of the West Saxons, in order to rob Edwin both of his kingdom and his life." [HE II 9]
And he nearly succeeded. Eumer presented himself at Edwin's court - which at that time was at the royal residence by the River Derwent. He gained an audience with the king on the pretext of having an important message from his king. Who knows why Edwin allowed him in - perhaps he needed a distraction; his wife was to give birth the same day to his first daughter, Eanfled, and he must have been in some stress, fearing for the safety of his wife and possible heir.
Whatever the reason, midway through delivering his pretend message, Eumer drew a knife from under his cloak and made a lunge for the king. The knife was said to be both doubled edged and dipped in poison so that if the blade did not kill him, then the poison would. Fortunately for Edwin, he had with him the most loyal of companions, one of whom - Lilla - having neither sword or shield to hand, nevertheless threw himself between the assassin and his king, paying the ultimate sacrifice for his bravery. Apparently the blow was so hard that the knife went all the way through Lilla and still wounded the king. One assumes the wound was superficial though as he made a full recovery. Eumer was then killed but not before he managed to take another thegn, Fordhere, with him.
So, how did this event bring about the eventual conversion of the first Anglo-Saxon king outside of Kent? Well, on its own, it did not but it can be said to have certainly played a part. Edwin had recently married a daughter of the Christian king of Kent, one Aethelberga. As part of the marriage agreement, Aethelberga had been promised the right to continue to practise her faith in Northumbria and had taken a priest called Paulinus with her for this purpose. Being one of the early Christian missionaries to England from Rome, Paulinus was not going to miss the opportunity to work on Edwin to try and convert him from his pagan idolatry. The fact that Edwin had allowed Paulinus to preach and had given him land in York on which to found his church shows that the king was open to new ideas but did not mean he was going to change his ways quickly and easily.
It took Paulinus a number of years and several artifices before he secured Edwin's baptism. One such opportunity was the failed assassination attempt. In response to the birth of his daughter, later that same day, Edwin gave thanks to the Gods for the fact that both the child and mother had come through the ordeal safely (never a guaranteed outcome in those times). Paulinus however claimed that it was because of his prayers to Christ that the birth had gone so well. In response, Edwin promised to give up his pagan ways and also to dedicate his new daughter to Christ if he would be granted victory against those that had sent the assassin.
Edwin then embarked on a punitive expedition into Wessex where we are told that slew or forced to surrender all those who had been involved in the plot, including the killing (as the Anglo-Saxon Chronicle tells us) of 5 kings (more evidence to support the view that Wessex was a network of tribes and sub kings, possibly under the aegis of a single overlord). Returning to Northumbria with the spoils of war, Edwin made good on his promise and gave Eanfled to Paulinus where she - and 12 members of her household - became the first Northumbrians to be baptised on the eve of the feast of Pentecost (6th June).
Edwin himself held on for a while longer, but it is safe to surmise that his resistance was crumbling because of events such as these. It cannot, however, have been an easy decision to give up the Gods of his ancestors not least because the king's religion would have also dictated the religion of his people in effect. Such a decision could not be taken lightly.