Definitely get the DNA test done even if it's only with one of them if you know for sure you only have sex with two then it's only one of the other so if the test come back not one you already know the other one is however you do know that semen last up to 5 days before it dies inside of a woman so whoever you have sex with first could also be the child that due to the semen lasting up to 5 days so find out when exactly you started ovulating in April or tell me and I added up for you
Incidentally, when was your last period in relation to sleeping with two guys? "In April," I get that, but do you mean before or after sleeping with the two guys? If after, then you should look to whomever you slept with after the period, nothing from before the period would matter.
Of course you need to do a DNA test, by a lab approved by the family courts in your area of jurisdiction, with both guys. You do not have the right to never seek to find out which man is the child's father: your child has the right to know and morally speaking it would be very wrong of you to avoid getting the answer.
Besides the moral issue and the child's right to know, which should rule since you are the mother and want to do everything for your child, legally speaking, a guy is not allowed to just say he wants "nothing thing to do with the baby" and that's that. Not being interested is not a get-out- of-child-support-free card. If a child is from him (biologically) he is obliged to help pay for its support whether he wants to act like a father in other ways or not.
I assume that by now you have figured out that when in January you were told neither you nor the other guy could have kids, the doctor (if it was a doctor) did not know what he was talking about. If the DNA test shows that the disinterested guy is the biological dad and the other guy wants to raise this child and doesn't care whose sperm produced it, talk to a lawyer about what it would take for the biological father /sperm donor to sign away his parental rights after the DNA test is done. (You might not need to go to this step since the DNA test might show that the guy who wants nothing to do with the baby is not the father. But you need to be ready.) I am not entirely sure if you can waive the child's future rights to the dad, but I think you can waive your rights to child-support payments in exchange for the guy waiving his rights to the child. Talk to the lawyer about all of this.
If you are saying you would like to hide from the more-interested guy that the less-interested guy is even a possible dad, I think you are not going to be able to do this. Since the two guys were in the same week, you aren't going to be able to tell just from the dates which guy is the probable dad.
If you think the disinterested guy is going to be a problem regarding getting a DNA test, the courts can issue a summons. Do this all with legal help, don't just try to handle things with drugstore tests on your own. You need to have it handled in a way that will stand up in a paternity suit in court.