I'm sorry, but with that few days in between guys, it could really be either guy. You weren't on birth control, and sperm lives 4-6 days in your body. You can be exposed to sperm whether a guy ejaculates or not: the fluid that oozes out of the tip of the penis when a guy gets an erection can also carry sperm from previous ejaculations. Showering does not remove sperm from your uterus or the tiny tubes that go from your uterus to your ovaries.
How did the doctors decide she was born at 38 weeks and 2 days? Was that from her size in a very early ultrasound? (Did you have an early ultrasound? When was it, and what due date did they give you?) Or were they merely calculating from the first day of your last period?
I just checked on your previous post, and here is what was said at the conclusion then:
If you really did ovulate around May 20, which a reading of the dates suggests is at least possible, then Guy 1 has the edge to be the dad, by a long way. But if your first ultrasound was not until your 19th week and your last period was questionable, there is really no way to be totally sure. If your only hard data is from an ultrasound in the 19th week, you have to add a week or even a week and a half margin for error either direction to any computed dates.
A lot of the numbers in your story suggest ovulation between May 20 and 23. Unfortunately, they could all just have been plugged in by the first doctor based on when your last period came, not from ultrasound evidence, and then not changed later. (You also said you weren't sure how reliably regular that period was, so if a doctor did make assumptions from it, the assumptions could be off.) If you have any evidence that the doctor reconsidered things upon seeing an early ultrasound, that would be helpful.