You can run it with no governor. A lot, if not most of us on here run everything ungoverned. Some don't like too. In my own experience, you can hammer on the smaller engines a lot more than the larger displacement ones as far as reving them up. The cast aluminum connecting rod is usually the weak link in this stuff but I've only blown up one engine so far in my life. A 4hp Tecumseh.
Some think the governor parts can come apart if unhooked from the outside without doing anything else. So there's two options for that. Either hook the governor arm with a spring to a stationary point on something just to keep some tension on it. Or take the bottom of the engine off and remove the governor parts, and then block off the hole. (or leave the shaft in the hole) That's assuming it's not the air vane type, I don't think too many are made that way anymore.
Something to think about is that, if your using a push mower engine, usually they have a very light flywheel because the mower blade acts as much of the flywheel weight. If the blade is removed, they can be very hard to start because there's not enough weight anymore. Prone to kicking back and ripping the pull start cord out of your hand. I've got them to start that way but it's not the most fun.
You might have good luck adding a heavy pulley on the crank or even a larger diameter dummy pulley just for added flywheel effect. Or if you have a flywheel from a horizontal engine that fits you could swap it. For instance, briggs 3.5hp push mower engines shared the same size flywheel as the 3.5 horizontal. Just that the push mower version is much lighter.