Normally you don't get much oil through valve guides unless the cylinders are sloping uphill - vertical crankshaft engines don't pour the oil through the guides. I doubt even Honda would put stem seals on a mower engine, and can't find any mention of them in the manual.
The most likely reason for your oil smoke is worn piston rings. Puffs of blue smoke on cold start are commonplace with mower engines if the rings, or the cylinder bore, are past their best.
Honda recommends automotive engine oil: SAE 10W-30, API rating SG or SF.