My first wedding was in France. Here, if you want a ceremony (religious or otherwise), you have to do it after the legal one. We're not religious, so like most non-religious people I know in France, we only had the legal one.
It has no walking down the aisle, it has no aisle. We showed up, there was a room with lots of chairs all facing a big desk, my future husband and I were sat in the front middle ones, our witnesses on either side of us, then our immediate family, then in the rows behind everyone else who had been invited sat wherever they wanted.
We were only ask to stand up and say "I do" (or rather, "oui"), the rest was the deputy mayor making a whole speech about what getting married meant.
Before it all started, two attendants who were the official witnesses asked if we were going to exchange rings, in which case they would have left room for that. We did not, which is also common (although usually because the people are planning to exchange rings in the second ceremony).
So, in short, nothing traditional occurred. We never wore rings because we didn't really see the point of them.
I'm planning to marry my second husband at some point. We already wear rings, because when I lived with my first husband and S and I were apart so much, it gave us something to be linked by. Originally my first husband Raga was supposed to get one too, but he wasn't present when we got them (spur of the moment) and I didn't know his size so I picked up a brochure, brought it to him and he was completely uninterested. So he never got one.
Sorry for the long background. My point is that we're going to use them as wedding rings, so we will be wearing rings, unlike my first marriage.
I'm also planning to walk down the aisle. I don't care that it started as a father giving his daughter away. I like the symbol of walking there as he waits for me. To me it's more about me showing up late than anything else, really.
I don't know who will walk me down the aisle, but the person who does will not, in my opinion, be giving me away. They will be there for support and to rejoice with me in that important event in my life. They'll be there to hold me back and make sure I walk there rather than just run and jump in his arms :P
Traditions might have an original meaning, sure, but in the end they mean what you want them to mean. Marriage was a property transaction but it doesn't have to be that every time. I plan to have ceremonies with anyone I consider to be my husband, regardless of how legal they'll be, and I see it as saying to the world "we've decided we're in this together, and we love each other, and we're committed to each other". And I don't think marriage is necessary but as long as people want to get married, I don't see why one should prevent them, either.