I think the easiest and fastest way is to have a large piece of steel block with a square edge, or a heavy vise.  Support the backbone of the sickle bar against the steel edge, or loosely held in the vise, and hit it the section to be removed squarely with a 5 lb hammer or similar.  The section will shear right off, and the remaining rivet stubs will either fall out our can be easily punched out.

Riveting the new section(s) on, put the two rivets in and support the bar on the the same or another heavy steel block and a few blows with the same hammer will spread the rivets.  You might need to put some small wooden blocks under the far ends of the bar, just to keep everything stable and aligned while working on it.

When I was a kid, I used to be able to pull the bar and replace and fix sections pretty quickly if we broke a tooth and didn't have a spare bar.  The hammer method is a lot quicker and easier than grinding and drilling the rivets. 

As was said.  Place the section in a vise that is just a little loose with the bar on the vise.  Give it a whack with a hammer and everything will fall into pieces.  I did a No. 3 blade this way, it took me about an hour to do the entire bar.

Make sure you put the bolts in the correct direction.  They are a pain to get back out after they have been tightened.  Don't ask how I know that!

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If I'm elsewhere and don't have access to mine, then as said above I usually just set the bar across a vise with the jaws slightly open, support the other end, and knock the rivets out with a punch, between the jaws. A socket underneath works too.

I have taken more than my share of rivets off with chisel and hammer leaving the knife in the machine. Then using a hydraulic jack as back up and hammering rivet, or one of the C clamp screw down rivet sets.

I never owned a Johnson Sickle Service but have taken a knife to someone  that did and replaced all the knife section.   With the bolt on method they have lost there appeal, but a real slick tool in there day. But the knife did have come off the header which I have seen be a all day job. At least by the time everything is straightened out so the knife goes back in with less than a big hammer.( more so on a combine head)

Another bit of knife repair that has served me well. If the knife breaks it is most always at the head. Take the broken piece and weld it on the other end of the knife. The weld is then only driving a few cutter section rather than all of them. You probably need a piece from another knife to get all the wholes in the right places and length to be right.