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I really have no intention for grabbing citizenship for my child.

Why not? By all means, get your child that US citizenship when you can legally get it, don't feel hesitant about it. Go for it!

Can I visit the U.S. while pregnant and what are the risks involved?

Although there are no specific regulations prohibiting pregnant foreign nationals from entering the U.S., entry is allowed or denied at the discretion of the admitting U.S. Customs and Border Protection (CBP) Officer. If the CBP Officer determines that you are likely to become a ward of the government (meaning that the government must provide medical care because you do not have medical coverage), you can be denied entry.

When determining if you will be allowed to enter the U.S., CBP Officers take into consideration the date your child is due for delivery and the length of time you intend to stay in the U.S. In addition, they want evidence that you have sufficient medical insurance to cover any medical necessities while you are in the U.S. and that you intend to return home.

If it is determined that you do not have sufficient medical insurance to cover any unexpected or expected medical care while in the U.S., you can be denied entry. Additionally, if you are pregnant and entering the U.S. at a border port of entry via vehicle, be aware the radiation detection portals deployed at the ports do not emit any radiation, and do not present a hazard to you and your unborn child.

Source: CBP

After that, all you need to do is to check with your airline about their policy of allowing travel in the late stages of pregnancy. All airlines have their own policies about the maximum allowed period before they refuse.

P.S.: I am trying hard to cancel my trip but it seems that it is so critical that if I skip this I might have to lose my job as well.

Come on dude! If it is healthy for your wife and unborn child to travel and it is legal, why on earth do you want to cancel? Only if you don't have enough medical coverage / means to pay for the medical costs you should think of cancelling this trip.