Formality at a wedding can be a good thing. There's something reassuring about sticking to certain traditions but one that seems to have fallen out of favour is The Grand March. Having played at hundreds of weddings I can safely say we've never see it done. I came across it on YouTube in the context of a Scottish wedding when I was searching for inspiration and thought that's a great way to start a wedding celebration. Being a tradition I should imagine it has the power to compel participation. You can't sit this one out! We've done many Scottish tinged weddings but have never started with the March. To give you an idea here's an example from a Scottish Wedding.
Some more Scottish folk enjoying a Grand March for the sheer heck of it.
After doing some more research I found loads of examples of Grand Marches from different cultures. Different moves, different tunes.
The English Country Dance version here is very similar but with the dainty chamber music (Playford styli?)
Looks like people just like doing a Grand March even if there isn't a wedding!
Sounds like it's a bit TexMex.
A tune called La Marcha de Zacatecas seems popular in New Mexico.
I think it's definitely something to consider.