Hope someone better educated on this stuff will chime in.

I'm pretty confident that if the replacement has the same mounting bolt pattern (although the deck is easily enough drilled for differences), is of relatively similar weight, dimension, and displacement (disp is better than HP ratings since standards are all over the place on this)... you'll be fine.

The most common misfit in repowering, besides cable routing, is probably blade mounting. You may or may not have the exact same taper, threading, splines, keyway, etc at the end of the shaft so you may not be able to use your old mounting adapter or even your collection of blades.

Assuming your replacement is vertical shaft it's most likely designed for mower duty. The "Heavy" flywheel may be a few oz heavier than the old engine's, or it may even be lighter! Is "Heavy Flywheel" emblazoned in flashy print on the engine cover? Just a guess. Like "6.5 PEAK HP" on your shop vac, it means almost nothing except hype. A chipper needs a 'heavy flywheel' but the spinning blade assembly constitutes this, not the engine's flywheel.

"Heavy Flywheel" might only be sales bling like "Rack and Pinion Steering", "Ventilated Front Disc Brakes", or "OHV" in flashy print meant to suggest to the buyer that his will be the only one in the neighborhood with such features. All three are as common as dirt today and useless descriptors in sales brochures.

Or I could be totally wrong in this case:)

It should?
I believe the "light" flywheel mowers had the blade bolted to the PTO shaft, so it also acted as a flywheel, whereas those with a blade clutch required the heavy FW.

I agree with both the above. If an engine is subjected to varying loads,increased flywheel weight helps maintaine rpms.

Heavy flywheels are usually used when you have a BBC.
This allows the engine to run smooth when the blade is not turning.
I would think there is no stop band on the Heavy flywheel unit.
Anyway, the engine will run smoother and most likely last longer.
And if the blade gets a little out of balance the heavy flywheel will counteract it.

The Flywheel is a combination of the flywheel fan/magnet assembly on top the engine, and the blade. As stated, on mowers with a blade that disengages (Blade Brake Clutch), the flywheel has to be heavier so you can get enough spin inertia to start the engine with the blade disengaged.