How to replace non IC-rated recessed lights in ceiling with IC-rated LED lights?

If the fixtures were installed prior to the drywall ceiling install, they are going to be 'new work' type. Which means they have an apparatus which is nailed onto the sides of the rafters above the ceiling. Without crawling around up there in the attic and removing them from there, it could be challenging to remove them from below without damaging the ceiling drywall..

Get you a piece of 2x4' piece of 3/4" thick plywood and lay it across the top of the joists so that you can snuggle over close to the lights, to work on them, without having to perform trapeze belly balancing.

If the cans are 'old work' cans, meaning they were added after the ceiling was already in place, then they would be a lot easier to remove and YES could be removed from below. Remove your trim rings and pull the light bulb shroud down. Do you see four black clips in the inside of the can, equidistance apart? If so, you have an 'old work' can and those clips can be tapped out of their locking positions, to allow the can to be removed from the hole.

If you don't see those black apparatuses and your'e looking a just a slick walled, aluminum cylinder...you have 'new work' cans and a trip to the attic is in store.

I am also guessing that you could chip away enough drywall to expose two outer edges of the can. And then, apply a large, jawed, clamp to grab those exposed edges of the can and squeeze the two walls together.

Squeeze the edges of the can together until there is enough space to get half a pair of tin snips to fit between the can and the drywall. Then, use the tin snips to cut away at the can and remove the pieces until you can get to the bracing.

If using the snips is too hard, use an electric metal cutting attachment instead. Then cut the cross braces and pull the rest of the remaining housing through the same hole.

Or, you could also just cut a larger hole around the housing, then cut and remove it. Then, cover the larger hole with a larger trim kit.