Are there non-religious wedding options for atheists?
Yes! There are quite a few options available for people who are uninterested or unwilling to have any of the traditional religious wedding ceremonies. Some are both nonreligious and without any real ceremony. Some include ceremony and ritual, but without religious elements. Finally, there are options which are religious in name, but not really in act.
As for the first option, couples always have the choice of a purely civil wedding, performed by someone duly appointed by the state like a Justice of the Peace. All you need is a license and a couple of witnesses, and the latter are sometimes composed of whoever is right there, just standing around. There need be no religious element at all it's just a simple statement of contractual vows which many atheists have found adequate to their needs.
Of course, such weddings lack so much of the ceremony and ritual which people (theists and atheists) have grown up believing are necessary for such an event; thus, it isn't surprising that a relatively small number of couples opt for it. Most want something special done to commemorate the day, some series of rituals which will help mark the transition from being single to being a couple. As a result, a number of non-religious wedding options which move beyond the simple civil wedding have developed.
Some of these are religious in appearance or name, but not really in act. What this means is that the wedding itself may take place in a church and may contain many of the familiar rituals which have a religious connotation for some. However, there is no actual religious substance or theme to the wedding. There are no religious readings, there are no religious songs, and for the participants the rituals themselves have a wholly secular meaning.
Finally, there are also wedding options which dispense with the general trappings of religion, even in appearance, but are not quite so plain and simple as civil wedding ceremonies. Such weddings are normally referred to as humanist weddings. The vows are written by the couple or by a humanist celebrant in consultation with the couple. The theme of the vows will focus on topics like love and commitment rather than religion or God. There may be rituals (like a unity candle) which have religious meaning in religious ceremonies, but now have a secular meaning here.
Humanist weddings are becoming more and more popular among atheists in the West. Such wedding ceremonies provide much of the emotional and psychological benefits which might be derived from religious ceremonies, but without all of the baggage which can otherwise come along. Such weddings also provide a familiar context which can make it easier for religious relatives who might be disappointed with a simpler civil ceremony.