Welding gloves...... I worked at a spay and neuter clinic to help my sister out (DVM). I'd use the gloves to take the cats out of the cages so they could get the shot to put them under. A two person job. And yes it depends on the weight of the cat for that.
As mentioned, talk to your vet. They will be able to give you something to relax it instead of putting it under.
The reason your cat hates the plastic carrier is because every tme it goes in to it something bad happens to it.
