This is a shot took from an episode, in which Ash's dad is supposed to be depicted
He doesn't look like Giovanni at all, but it is probably due to the young age of the man, then ,with the time goes by, his aspect could have changed in the actual form.
Otherwise he can be another man that we don't know.
I don't support the Oak theory because the Prof. doesn't seem too much worry about the danger that Ash can eventually encounter during his travel; but he has a "particular" relation with Delia, that's true, perhaps he can be a "new pretender" for the middle aged lady.
Another important point is to understand if this hypotetic dad is still alive or not; in the second episode of the first series we can guess that is still "between us" thanks to the conversation of ash with his mom.
Otherwise the Father is dead but nobody has said it to Ash not to shock him (we must remember that he's 10) and this could explain also the "light" sense of protection of Oak that someone before me has pointed out; another proof of this supposition could be located in Ash's behaviour with girls, he isn't ever seemed interested in them so he hasn't recived any teaching about " how to approch to a female person" because off the lack of a "male figure reference", although I bet that a 10-years-old child doesn't think about this kind of "dirty stuff"