I don't mind shopping, but prefer to be on my own if I'm going to enjoy it.
I hope you find something you like and that fits well. I believe your happiness (and Mike's) on the day is all that matters and if you'd be happy walking down the aisle in flats, go for flats. Or even sneakers for that matter. If you have a long dress, chances are no one is going to see your shoes unless you show them anyway.
My cousin's kept the shoes she was wearing a secret until the day, cos she knew someone wouldn't 'approve'. They got a shock, but it was too late for them to do anything, so they had to accept it. My cuz wanted to be comfortable, so she wore chucks. Only the bridal party knew until after the ceremony, when they become a talking point, in a good way.
If you have trouble with sizes and fit, unless you know the brand well or had shoes from them before, I'd steer clear of buying shoes online. Shopping in stores may be something you have to grin and bare, but maybe do your research if possible on the online before you make a trip to the store.
Good Luck!!!