Unity candles are very big in the US, although it is unclear where it originates from – evidence indicates it may well be a far eastern tradition. It's a symbol of uniting yourself and your husband as a couple and also uniting you as families.
There are many different ways of incorporating a unity candle and as it has no 'religious' connection it should not interfere with anything.
You do not say if your parents are going to be there as it usually involves them as well as your family. The general just is that you have a main personalized candle called the 'pillar' candle. You and your partner each have smaller candles or tapers which are lit by your parents. You then light the pillar candle. Each close member of the families (parents, children's, brothers and sisters) have an individual candle or taper which they light from the pillar candle and recite a passage as they are doing so.
All of this is normally done after the wedding ceremony.
As an alternative you could light each others' tapers or candles (I think that individually personalized candles would be a nice keepsake to put with your pillar candle) and then both light the pillar candle together, reciting a hand written piece that is personal to you . For example the two flames are yours uniting and becoming one as you light the candle together etc.
If you like I can write something and you could add your own lines to personalize it. It does not have to rhyme or flow – just make it your moment.
There are lots of websites who make personalized pillar candles but for your individual candles, I suggest personalizing them yourself. You can either personalize your own or do each others by engraving their name and symbols, rubbing the candle with a favorite spotted oil, decorating with personal items and ribbons of a favorite color.
I know of a couple who purchased a candle-making set and make their own candles by adding her in her favorite flower petals and some curls of hair for her and she put some cut hair from him in the scent in his
Of you make / decorate each others be sure to focus all of your love and good intention into it. When they lighted the pillar candle they each let some wax drop onto the candle from their heads to complete the ceremony.
But if you really do not want to go that way then you can always go the same way as most couples do You can either print the vows / readings out on a card or ask the captain to read it out and you can repeat it. A lot of couples do this as it takes the pressure off and there's no worry of mistakes!
But there are a lot of couples out there that would rather tell each other what they mean them, then have to stay there and repeat what the captain just said. For me I would want to be able to hear from him / her what I mean to him / her then having them say it to me.