I realize this is an old thread that has been resurrected, but I thought I'd chime in anyway in case someone else had this same question.
A wedding is supposed to be personal. There are certain "elements" that people expect to see, but people really like it when a couple makes the ceremony their own. If you're not doing an all out circle casting/element invoking/god and goddess mentioning kind of ceremony, then no one will really notice that it's a pagan ceremony and not just a personal ceremony. (Btw. I have ZERO problem with a circle casting/element invoking/god and goddess mentioning ceremony, but that's not what the question was about.) Do your wedding the way YOU want to do it.
For my own wedding I did a lot of personalization, and included enough pagan elements to satisfy my religious side. However, I felt that the ceremony was more of an expression of DH and I's commitment to one another, rather than a strictly religious experience only. The basic layout went like this:
We had a wedding arch set up outside in front of a fire-pit, with an altar set up to the side with various things on it - to include our rings, handfasting scarf, and a necklace we gave to DD. The officiant came early, and smudged the ceremony site, set up the altar, and when we walked down the aisle there was still incense burning.
-Family walked down the aisle
-DH walked down the aisle
-DD as flower girl walked down the aisle to hold DH's hand
-I walked down the aisle on my Dad's arm. (Well, we danced a little down the aisle! haha.)
-Dad handed me off to DH, and then we each took DD's hand under the wedding arch.
-Female officiant had everyone be seated, welcomed everyone to our wedding, said a little something about our decision to marry and create a family with DD.
-DH and I each said vows to DD and then presented her with a necklace that was on the altar.
-We then did a modified version of the hand blessing (no mention of deity in my version)
-We exchanged rings that we took off the altar after our hands were blessed
-Then our hands were fasted. Officiant explained a little about this, but in a non-religious way. More of a this binds them hand to hand, heart to heart, life to life, kind of way -- but different language.
-While our hands were still tied, the officiant read the "Apache" wedding blessing.
-Officiant proclaimed us handfasted, and said a little something about the circle of the knot-ed scarf as she took the unbroken circle off of our hands.
-We were announced husband and wife.
-People blew bubbles as we exited.
Everyone couldn't stop talking about how lovely the ceremony was. I had a few people say that it was "modern." And a couple of the guys joked that we "really tied the knot" with the handfasting. No one said a single word about religion in relation to the ceremony at all.