It is certainly more likely by a ways, for it to be the second guy. But if she slept with someone three days after her period ended, he still has to remain a candidate. Some women do ovulate as early as day 8 from the first day of their period, and sperm can live in the woman's body for four to five days after the sexual activity. Unfortunately, him not ejaculating in her vagina is not enough for certainty, unless he was also wearing a condom.
So, chances are, as you already say, that the one with whom she had a lot of unprotected sex at mid-cycle is the daddy. But a DNA test is going to be needed to be sure.
The second guy is the father. It is NOT the "Wednesday guy."