I think the ROM link above makes it clear that it is not proper to do it after the traditional/religious ceremony.
You can have the solemnisation after the first march in and just before the wedding lunch - that's what I'm doing. Just choose a solemniser that is chop-chop, the whole thing only takes about 15 mins and your guests, especially closer ones, can witness the ceremony which is quite meaningful. (and also convenient for them as they don't have to come a couple of hours early for it if you hold it earlier in the morning.)