You'll be fine. My dh was just the same - we had a very difficult time during the first pregnancy as he was scared shitless and was dreading the birth. For about 3 months after dd was born he was pretty much in shock and spent a as much time away from us as possible. I've never felt so unsupported in my life during that period. I also had pretty bad postnatal depression, which wasn't caused by, but certainly was made worse by dh's attitude.
Fortunately once dd started to smile and interact more as she got older, he felt more involved. I had to go back to work when she was 5 months old, and dh's job had just ended, so he was a sahd with her for 3-4 days a week. They got on famously and now are incredibly close. She just adores him!
We now have ds who is just turned one, and dh has been a lot more honest about frankly not feeling that involved for the first few months. I can, thankfully, see them getting closer and closer as ds develops.
Dh is still a sahd to them both for 2-3 days a week and he is brilliant at it. I think the fear and feeling useless is very common in men, but men tend to get completely sidelined during the whole pregnancy/delivery/baby period, tbh, and get very little support.
We have been through a difficult couple of years but are feeeling finally that we have the child-rearing thing slightly under control now! It's the most difficult job I've ever done, but most rewarding too.
Even if you feel numb, you can be a fantistic support to your dw by keeping her fed regularly (!), making lots of drinks, keeping the house clean and tidy (I know everyone says it doesn't matter, but I used to get very anxious about this). Get a sling for the baby, the wraparounds like Moby are great and sooth the baby by being close to you. Good for a walk or for doing things round the house with baby in tow.
Although you'll probably be surprised how often a newborn will sleep, just make sure you are ok changing a nappy and giving a feed if you are using formula or expressed breast milk. Make sure your dw can get the occasional break, even if it's just a walk to the shops, a candlelit bath, go to get haircut, etc without her having to fret that you can't cope for an hour or two. If you are lucky enough to have family or close friends nearby, then take advantage of offers to babysit, even if just for an hour or two, so you and dw can have a walk to the pub for a sit down and some time together. If not, then try as hard as you can within a few weeks to get some time together in the evenings just to eat dinner together and relax as a couple.
Good luck, and don't feel bad if you feel like a bomb has hit your life and relationship for a while. It has! You just get on with it and eventually realise after a while that the bomb was a good thing.