Such matters are always "alleged" until they are proven dave, no matter how blindingly obvious (or not) the facts seem to be. Go to any court and you will see "obvious facts" referred to as "alleged" and anybody referring to them without that prefix will be pulled up. Courts are there to determine what is alleged and what actually happened.
//He said / she said. No other witnesses.//
Which describes a huge number if not the majority of domestic violence incidents. Are you suggesting they should not be pursued?
//I don't think a slap would of itself cause a filling to come out and leave no other sign.//
No, neither do I but we don't know what really happened.
//How could a conviction be obtained?//
In the same way as any other. If there is sufficient evidence to convince the court "so that they are sure" (or "beyond reasonable doubt" in old money). That evidence can consist solely of the testimony of the (alleged) victim, as it often does in such cases. Just from a personal viewpoint (based on nothing but guesswork) I would suggest this is more suitable to be charged as Common Assault rather than ABH. For that charge to be made out, not only does there not have to be any signs of injury, there does not actually have to be any physical contact at all.