Tier 2 Dependant Visa for baby born out of UK

Hi,
I do have a question.
I am on tier 2 visa, and my wife has a tier 2 dependant visa, we are expecting a baby in the next few months, but my wife will deliver in Egypt, not in the UK.
How hard will it be to get a tier 2 dependant visa for the new child? Do I have to be in Egypt to apply for him, or my wife can do that?
Also, will I have to pay the IHS surcharge for him? and If he is to be born in the UK, will I have to pay it?
Can anyone help me with the process in this case, especially if any has done the same?

Thanks

https://www.gov.uk/tier-2-general/family-members - this answers most of your questions. I do not think you need to pay for giving birth to the baby in the UK since you pay NI contributions and have free NHS. But it is better to find out with your GP or at the birth location https://www.nhs.uk/conditions/pregnancy ... ive-birth/. Actually your wife will be eligible for Maternity allowance or Statutory Maternity pay - depending if she is working or not. Please read here https://www.gov.uk/maternity-allowance. If you have children while you’re in the UK, you can apply for permission for them to stay. If they are born outside the UK you will need to apply for their PBS dependant visa. You do not need to be there.
You will need to pay UK healthcare surcharge for you child.