If the OP is convinced that his son has reached a turning point because of what has already happened since the event then I can understand the doubts he now has about pursuing a prosecution. A number of posters have offered sage advice about attempting to get the case dropped and if he has no previous convictions then I think the effect of the OP & authorities actions so far is probably going to be of far more value than a prosecution (and more importantly, a criminal record.)
As the charge was common assault as opposed to the more serious alternatives, then the OP as victim has a say in what is proposed. It is common for a victim of violence, particularly in a domestic setting, to retract their statement and say they no longer wish to support a prosecution. It does not mean that the case will fail but it will be considered. A lot will depend upon whether the son has admitted what happened when interviewed but given this is the first time that the OP has reported such a thing and there is no previous history to warrant a victimless prosecution, then there is a chance that the CPS, if informed by police/defence, will not proceed.
It also depends on whether the son has already entered a plea.
Some kids change and sometimes all it needs is a wake up call, others don’t and it is the OP that needs to make that judgement. He also has to weigh up how he will feel if his son does get convicted and receives a custodial sentence (unlikely but due to the aggravating aspect of the knife, not impossible.)
Hope it all works out for you.