Personally I would go, just so that in the throws of labour (which might take hours but equally might happen very quickly!) you are not worrying about what the procedure is at this new place.
They will tell you what signs to look for, when to ring/go in (and when not to - or they will send you home!).
You will also know what is available in the rooms and what you are allowed to take in. E.g. I had wanted to take music, but we weren't allowed to take any mains electrical equipment, so had to take batteries.
Also they will tell you the policy on DH - is he allowed to stay overnight/what time he has to leave, is there somewhere for him to sleep if you give birth at an awkward time, or do you need to take a blanket for him etc etc.
Plus the one thing that will be very different between this and the C-section is the pain relief that is available. It's important to know that there are time limits on what you can have - e.g. you might have to pre-order an epidural if you think you might want one (have heard stories of it being too late or no anaesthetist being available). Plus don't you want to know if they have birthing balls/pools, a bath, tea/coffee, radio, etc there for you to use?
Labour can be pretty testing even at the best of times, so the last thing you need is to not know the drill for this hospital and end up flapping around not knowing what you're meant to be doing (or worse, your DH flapping about not knowing what HE is supposed to be doing, and you having to sort HIM out when you are trying to breathe!!).
The way I see it is - the more informed you are, the less stress you will be under and the easier things will be. The paperwork can wait for one day, surely, just for your own piece of mind? You might get there and find they tell you nothing you didn't already know, but at least you will know that you have all the information, instead of how it is now, where you really don't know one way or the other.