The Anglo-Saxon Chronicle A version, under the year 648 states that Cuthred was the son of Cwichelm and Cwichelm was the son of Cynegils (so he does need to be detached from his current father) and I haven't found anything so far that disagrees with that family line-up.
The Wikipedia article is basically pretty mixed up. The article they mention by Kirby is actually D.P.Kirby, 'Problems of Early West Saxon History', English Historical Review, 80 (314), pp. 10-29 and from a brief look it doesn't see any problems with Cwichelm, but does see issues with Cynegils parentage and thinks there might be two people with the same name.
Also the section in Wikipedia about the latin terms makes even less sense, since the Chronicle was originally written in Old English and the Old English is clear that the relationships were as above. See here
So by all means change the father for Cwichelm, but seems to be no reason at all to delink him.
I would also change his date of birth to about 600. Although that makes him only 14 or so in the first battle, naming Cynegils and Cwichelm together may be more of an indication that Cwichelm was the heir apparent rather than he had an important part in the battle.
Kirby does make the point that the chronology of this group of West Saxon Kings is a bit out and making it about 600 may make that a bit more understandable.