I take a drill and a 7/8 inch bit and rotate the shaft. Starts the mower in seconds. No pulling your guts out, no heart attack, no sweat. Here's how I do it.
I have 3 old junk Murray mowers (old red painted Walmart stuff). I take the shrouding and all the safety oriented crap off them. I mainly just take my angle-grinder and cut away all that crap, like taking a can opener to a tin can. This exposes the shaft end which is on top of the push lawnmower. It is a square, nut looking deal --the top of the shaft. It fits a 7/8 inch socket.
Now, I take a drill bit that will "chuck into" the other end of that socket. I use a half-inch spade bit that fits fairly snugly in there. All I'm trying to do is to get something to allow the drill to turn that socket that I put on the square shaft. I then hit the primer (rubber bulb dealie) on the lawn mower, make sure it's in the "run" setting. I put on my earplugs, I use the ear protector deals that go all the way over my ears --like they use for shooting guns. Then I press the drill ON button and let er rip. Hold the drill FIRMLY so it won't pop out of your hands. The lawnmower motor turns...I'd say about 200 RPMs. And very soon she STARTS. Usually, it immediately pops that socket off, onto the ground. Sometimes I smack that socket off the (running mower) shaft, with the drill spade bit. Don't be stupid and try to grab it with your hand, to take it off the mower.
I usually run the mower till it's outta gas, or if the "kill" button still works, I shut it off with that. It makes the job a little more fun this way. You think back to all those years (each year...getting older and fatter and more exasperated) when you wasted time tuning up the mower and changing plugs to try and get it to start, fiddling with all those idiot levers, pulling your guts out in the sun, it still didn't start, refiddling with the settings and trying and trying. Those days are DONE. Just stand there a few seconds or even a minute or two with your drill doing all the work for you, as your old balky mower finally gives in and starts...time after time. The EASY way.