With that further information, I would suggest that you buy or borrow either a cylinder leak down appartus or a spark plug hole/air hose adapter. Pressurize the bad cylinder after firmly blocking crankshaft movement while piston is at top on the compression stroke. Pressurize the cylinder and listen for where the air is escaping. If you hear it through the exhast pipe, an exhaust valve is leaking. Through the carburetor and an intake valve is leaking. Through the oil fill hole and it is leaking past the rings indicating that you have cylinder/ring/piston issues.
If it DOES turn out to be damage in only one cylinder, there is absolutely nothing wrong with repairing that one cylinder only. If the engine is just generally worn out, then you will, of course want to overhaul both cylinders.
These engines are new enough, that I expect pistons/rings and any other engine parts to be readily available. When I've rebuilt small engines in the past, it always seems to be ones that are old with difficult parts availability.
Hope this helps,
Larry