I'm guessing you're not in the US, where the "legal documentation" part takes all of about 2.5 minutes to complete and authorize - you have to go pick up/pay for your license a few days in advance, but otherwise it's done, so it's generally done on the wedding day.
How long does it take to do the legal bit where you are? If you are having your wedding ceremony on your anniversary date, then try to schedule in the legal bit in the morning (for an afternoon/evening wedding) or later in the day for a morning wedding.
Otherwise, I don't see anything wrong with doing them on separate days.
EDITED: OK, I thought you were in one of those countries where your religious ceremony doesn't count legally - some places require you to have a civil ceremony before a judge in order to be legally married, plus one in a church to be married in the eyes of God. LOL, my bad.
Depending on where you live, you will go get your marriage license before the wedding day (on a business day, during business hours) and pay the fees, show your IDs, etc. Most states have a waiting period of at least a day but some don't, and most have a valid period of at least 30 days, so you can get it anytime during the validity period- you can find out here the requirements for your state here:
http://marriagelaws.info/
At your wedding, your officiant will do all the legal stuff (you sign the license, as do your witnesses if needed) and then you or your officiant will send the completed and signed license into the state for filing. Again, the license must be received back by the state before the validity deadline has passed.
If your officiant has done a lot of weddings, s/he will know exactly what needs to happen in the state you're marrying in. Good luck!