Congrats!
We did the same thing for similar reasons ie: "government wedding" and "real wedding" and it IS really hard not to be giddy and excited at the first one... we did the same thing all day "hello husband" etc. And the shock (surprise really) of it, at least for me, because it's easier to
think of it as necessary paperwork than it is to
do it as such. So you don't prepare yourself - but then "waaaaait a MINute! We just got married!"
So yeah, it is cool and amazing to be (legally) married - but if you decide to keep it separate in your head, it IS possible and the "real" one will be just as romantic and meaningful as you want it to be.
For me at least, this means that we've gone back to referring to one another as boyfriend and girlfriend... so that our "real" wedding (not until September!), the one we build up to in our minds, the one where everyone important to us can be there, and the one where the true commitment is made - is the one where our married life begins. That being said, we might secretly celebrate our first one too... but maybe more as a fun part of our lifelong story as opposed to our wedding anniversary.
Anyway, sorry this is so long, but I wanted to reassure you that you are not alone, it IS very odd, and if you want to separate things, it's possible
Best of luck to you!!
(PS - we got "married" in a chapel/shed in someone's backyard - the only person that could do it on our really short notice
Muzak and all... it truly is bizarre how little where you are matters once you start saying the words!!)