Any suggestions on how to handle this?
Tough call. Not inviting one person will surely be noticed, even more given that person you say is friends with most coworkers.
I see two options here:
You could decide not to invite that person to your party. In case you were asked why you could say you "forgot" to invite him. This however is a bit dishonest to my taste. Also have in mind that if it is known that you don't really like this person your other coworkers most probably expect you to be reluctant to invite him, and probably won't be asking questions (unless they were not that aware of your situation with this person or if they have other intentions on asking).
Now, I ask you: Is it really unbearable for you to tolerate this person? The other option you have is to invite that person anyways. It is your party, your moment of celebration with your partner and friends. Usually in most parties one goes there are people you like and people you don't, but you should try not to be affected by their presence, and enjoy the moment as it is.
If you think you can tolerate his presence for one party then I suggest you invite him. Who knows, it could even be the case that he does not assists at all (for whatever reason he may have), but you will have made a honorable choice, and if other coworkers ask you can say "I did invite him, probably could not come, it's a shame"
If you go for this second option, a side suggestion I have is to be clear with him when doing the invitation. You could say something in the lines of: "Hey, I know we have had some problems on the past, but I wanted to invite you to my baby shower. It would be nice to share a good moment with you and our coworkers". This way you are making it clear that you don't want any problems during the party, but at the same time you are showing respect and offering him your forgiveness, something honorable and showing signs of maturity (which will also help your reputation as a plus). Hope this words help you out, and my best wishes to you and your new family.
Note: As someone pointed in comments, it is worth noticing that it seems that baby showers are mostly events where only females attend. If you think this is possible it would be worth a try, as you will be solving your dilemma.