I am almost certain the shaft in my boat is 3/4". It definitely isn't 1". I don't buy that the larger shaft is necessary to reduce vibration. I'm sure it would be a nominal improvement, but I would first look issues like the cutless bearing, shaft alignment and motor mounts before I began to even consider beefing up the shaft. If there is enough abnormal vibration to cause you to wonder, I would bet that the cause is one of those symptoms rather than an undersized shaft.
If it aint broke, don't fix it, right?
(Or, on my boat, if it aint broke, don't use it.)