Do. It even discuss the birth certificate with him. Don't put his name on - and if you don't tell him he's unlikely to know the ins and outs anyway so won't be able to turn up (visa being an issue too assuming he's not one of the "elite").
I'd be inclined to take him on his word. He doesn't want to be a father and he knows you're going to have his baby. It's not up to you to keep him up to date, keep in touch with him. If he wants to know he'll ask. He knows how to get in touch with you. You cannot facilitate fatherhood for him, it's something he has to actively choose, if indeed he changes his mind. But still don't put him on the birth certificate. He's - visas aside - allowed any contact you allow with the child one day. If he's signed as a parent then you'll have to get permission from him for lots of things that will impact your life for the next 18 years. You had a fling, you didn't sign up to have him control your life.
Focus on yourself, surrounding yourself with the people who truly care about you. Focus on your pregnancy. Do things like organise photoshoot of your belly, sleep a lot etc. Make this a pleasurable time for you. Don't spend it thinking about someone else. He's missing out and it's not your job to ease that.
And be aware that you are probably better off without him in the picture. Even if he's the most incredible guy, there's a cultural background - that it sounds like you're not from - that will view you, and likely your child, badly.
Also don't tell him the exact due date. If you have then if it ever comes up point out it could be two weeks on either side, or be vague. Whatever emotions he'll be going through, even if it's indifference, keep a barrier between you and him, for protection.