I think that the Suez channel has no recent upgrades, but the Panama channel is currently being expanded, and the expansion cost a los of money and a lot of CO2. And there are some projects to build a channel in Nicaragua ...
It's hard to find reliable numbers for the weight of a TEU, but I'm seeing references to a "maximum gross mass" of 21 and change metric tons, and an empty weight of 2.4 mt. Let's make the math easy and suppose each of the 15k TEUs on a single ship are filled to half capacity, netting a little under 140000 mt.
The "long way" is some 3500 extra miles, which, at .04kg/ton-mile, is 1.96 million kg, or 19.6 thousand (metric) tons of CO₂. Per ship. Per trip. And that's just the extra emissions for going the "long way".
For sake of comparison, the notional "average" car emits about 4 metric tons of CO₂ per year.
I have no idea what the maintenance costs of the canals are in terms of emissions, but they'd have to be amortized across every ship that traverses them. Per another poster, almost 17.5k ships sailed through the Suez Canal in 2015, so you're looking, with very back-of-the-envelope math at a little under 20000 metric tons versus 1/17500th of the annual maintenance emissions for a ~200km long canal. For a single ship's passage through the canal.
The construction costs of a canal, on the other hand, have to be amortized across every ship that has ever traversed it. The fractions get ludicrously small there (though they are, admittedly, of a rather larger number).
Without knowing the actual emissions numbers for construction or maintenance, I can't be sure, but I'm going to go ahead and predict a clear winner...
EDIT: Corrected some bad inputs to my math. Please, someone double-check my calculations. It is, after all, the end of the day on a Friday. My brain may be a smidge soft...
It's far from obvious that CO2 emissions from excavating millions of tons of sand and earth would be dwarfed by the savings in the transit emissions of high-tonnage freight ships, which, unless I'm much mistaken, represent by far the most efficient means of transportation humanity has ever come up with.
OTOH, I assume there weren't many bulldozers in the mid 19th-century (I actually have no idea how suez was built). But, it's not really reasonable to just throw human power at something and declare it CO2-friendly.
And here's the bottom line. For better or for worse, externalities don't actually count. You can piss in the pool. People banding together and deciding otherwise - when their ancestors have gotten most of the pissing their hemisphere will ever need to do out of the way, and the rest of the world is still clawing their way out of abject poverty - is... maybe well-intentioned, but don't hold your breath. Poverty is really fucking awful. People on their way out of it will not tolerate if their governments try to put on the brakes because they watched an Al Gore movie. It's just not going to happen.
The good news is that the consequences likely aren't going to be too severe. We're not facing extinction (that many other species are is irrelevant, that ship sailed a long time ago). Florida goes away, sure. Indonesia loses a lot of it's land area. It's not going to happen overnight, people are not going to drown. They will move to higher ground. And at the end of it all, you have a world population that's not poor. That's a good trade, and I have every confidence in humanity's ability to manage whatever other consequences follow, we're pretty damn good at making tough decisions once we have something to lose. But right now, that's just not the case, except in the developed world.
I think that your confidence is a little too high on this one. It's very possible to paint yourself into a corner that no amount of magical economics "a solution to any problem will present itself if the price is right" thinking can get you out of. You sound like a politician making appeals of "smart people will work out the details of the impossible promises I'm making."
According to numbers I found, an "average" bulldozer burns 4 gallons of diesel an hour, yielding an annual emission rate of around 66 tons. Let's assume for sake of easy math that other earthmoving equipment has a comparable enough emission rate that we can just call it the same. If it takes 10000 pieces of earthmoving equipment 10 years to dig a canal (a complete wild-assed guess, admittedly), that works out to 6.6 million tons of CO₂.
Per my previous comment, we'd established a long-way extra emissions rate of ~20000 tons (19.6k metric tons is 19.9 and small change thousand long tons; call it 20k for easy math) per ship, per trip.
Remember that, to calculate whether the canal is a "clear winner" in terms of emissions, we have to compare the emissions saved by ships using the canal, not the extra burned by ships that don't. At 17 and a half thousand ships in 2015, saving 20000 tons of emissions each, that's 350 million tons in 2015 alone — over fifty times our estimate of the emissions from constructing the canal.
Yes, it's WAG envelope math, but even if we up the estimate by an order of magnitude — 100000 pieces of equipment over 10 years, or 10000 pieces over 100 years, or however you want to factor it out — that's still a five-fold win, in just one year. On a canal that's been in operation for some 150 years.
So, yeah. Unless someone can offer better numbers than I have, I'm going to run with "clear winner", thanks.
All that aside, I'm not even going to attempt to rebut to your naïve optimism over technology and good ol' Team Humanity's problem-solving spirit coming along to save the day, or your blasé "Extinctions, shmextinctions" tone. They're, IMO, premised on beliefs so divergent from reality, they don't even warrant the effort.
That ship sails only when every other species on Earth is extinct. And humans would be extinct long before that happens.
Biodiversity isn't a "nice to have." It's essential for our long-term survival on Earth (or any other planet/space colony, for that matter).