I use the old buckets mostly for working with cement. A good handle makes carrying the heavy buckets a lot more enjoyable.
Step 1: Removing the Handles
The wire is springy. To forcefully remove the wire you need to grab what you can of the wire at the first bend with a pair of pliers and give the wire a twist. That lets you slide the end of the wire back out the hole.
To get what's left of the old plastic off, beat it with a hammer, cut it with snips, or use a hammer and chisel. Sometimes you can just rip it apart with pliers.
Step 2: Cut the PVC Pipe
The wire has a sort of recessed area where the new handle will fit. Cut the pipe to a length that fits in this recessed area.
Step 3: Bend the Wire
After you get the pipe section in place, bend the end of the wire back to 90 degrees, the way it was to begin with.
Step 4: Replace the Finished Handles
You should now have no further problem with the handles. Also, because of the increased diameter of the pipe, carrying the buckets will be a lot more comfortable for your hand.