Probably the Welland Canal goes a little differently because removing the War of 1812 means you change the life of William Hamilton Merritt, who may never buy property in Shipman's after his service in the war and may never buy a sawmill that hungers for canal water, and therefore may never petition for it. But you still have the basic problem of how to get goods past Niagara Falls, and you still have the likes of John DeCew living in the neighbourhood, who does own a mill in the area prior to the war. Prior to the canal, you have a system where ships sail a little ways up the Niagara River, stop before they get to the whirlpool, and hire guys in Stamford to portage their ship and goods up the Niagara Escarpment and back to the river. You can keep doing that for a little while but eventually the volume of commerce will increase and the size of ships will go up, and the portage won't do the job anymore.
The nature of the canals will also change: Bear in mind that the current canal is actually the fourth Welland Canal. The original was a series of little wooden locks following Twelve Mile Creek from Port Dalhousie and on up the escarpment to the Welland River - it wasn't straight through the peninsula. Eventually a canal straight through the peninsula is probably inevitable, especially if future development predictably continues to lead to more and more massive ships which couldn't really navigate the Welland River, but there are significant butterflies in the development of Niagara - the shantytowns that turned into the various parts of Thorold may be somewhere else, though the development of a Port Colborne analogue is probably inevitable. Welland likely is too because it's at the juncture of the first Canal and the river, though its name may be different.
Even if you butterfly Merritt, you likely just get a DeCew Canal, and a lot less things in Niagara named after Merritt.