I like subway, and often have lunch there.
But I agree day old subway subs would be pretty nasty - damp, soggy bread that's stale at the edges, and limp vegetables, cheese that's going slightly mushy.
I think you can phone in the order, and then you could pick it up between the baptism and lunch. I'd avoid the saucy subs (meatball, etc) ones that are intended to be eaten hot (steak and cheese) and tuna. Stick with the cold meat variations.
I'd go for a 12 inch sub per person if you have reasonable sides - chips, veggies and dip, some dessert, etc. Get a couple extra if you've got heavy eaters.
An option that would work better to pick up the next day would be to stop at Costco the evening before and get rolls, veggie, sliced meat and cheese trays, some squares or cookies, dip and a bag or two of chips. Provide butter and mustard, and maybe a jar of sliced pickles, and you've got a much fresher meal.