The hardest part was cutting the old axles with a hacksaw after I lifted the rear with air shims. I had to feed the new axles from the inside toward the outside, with the flat part of the axle on the inside, because it's impossible to go from the outside in. There is not enough room to straighten the axles enough to feed them through, so I had to make special accommodations.
On the right side, I used a screwdriver to gently pry up the condenser drip pan just enough to get the axle under it and straight enough to feed through the holes and the new caster. On the left side, I had to use a socket (1/4" ratchet 12mm socket IIRC) to remove one of the bolts holding the compressor to the bottom of the fridge (and surrounded by a rubber bushing). With that out of the way, I was then able to straighten the axle enough to feed it through the holes and the new caster. The bolt easily ratcheted back in place. There is no nut underneath to worry about.
Other how-to videos and reviews state that it is necessary to drill holes in the axles and use cotter pins to secure them in place. But, I had no trouble whatsoever with manually crimping the open ends of the axles with a channel lock so that they stay secure. That was so much less work than having to drill and manage cotter pins.