The amperage on the motor is probably more honest, and if it is from a residential treadmill, 15 or less. 1.5 actual HP at the very best, if it is 15 amp and the motor is efficient.
4.5 actual HP is way overkill for a treadmill for anything less than, say 4.5 horses...
I think the "shop-vac" HP ratings come from stalling the motor and measuring the current right before the motor burns out (which might be 50A very briefly). It can't even do that plugged in to 110 at your house because the breaker will trip at just over 15A. Note that by definition, the motor isn't doing any work at all when stalled, it is just turning electricity into heat very fast until the windings melt.
Anyway, not trying to rag on you. I am very interested in the forge and grinder and how they work out. 1-1.5 HP will be plenty for knife grinding in any case.