On the right track but not as simple as that, 2 days of a vigorous ferment gets the unwanted elements from the beer evacuating with the co2. Cap the ferment using a spunding valve and pressurise the beer.
Now you come to the tricky bit, you can't just put a pressurised vessel into a cold crash, I think someone on a thread here posted a pic of their s/steel fermenter which was sealed and the lid sucked in due to the co2 being drawn back into the beer, put your snub nose in, leave it for about 20 mins and you will see what I mean. I counteracted this by putting an expandable plastic water bottle filled with co2 connected to the gas post of the fermenter, so as the gas is drawn into the beer it is replaced by the gas I had collected. Or you could just use gas from a bottle.
And there are even more not pressure fermenting. Terri Fahrendorf a brewer, laid out solid ground rules for carbonating under pressure. Which is what almost all the pro brewers do to carbonate their beers.