Okay, the answer is YES.
The new-style K3-K4 wheels/tires 42710-VE2-M00ZA will indeed fit and work fine on older K0-K2 mowers just fine.
The original K0-K2 wheels/tires 42710-VE2-800 are semi-pneumatic and made from real rubber, thus very costly.
42710-VE2-M00ZA tires are made of PVC (much less costly).