No, this is the best route. Your train to Levanto may indeed arrive late, but if you miss your connection, just take the next regional train on to Vernazza. Trains that stop in Vernazza are "locals" - so you need to change trains in Levanto, Monterosso, etc. (where the faster trains stop too) to transfer to a local. There should be plenty of trains on to Vernazza.
I don't recall if you need to change platforms at Levanto. It's a small station - maybe three platforms total. There are only two tracks, one going north one south. The train to Vernazza goes in the same direction (south) as the one you'll get off of, but I'm not sure if it will use the platform on the opposite side of the track.
If you have a smart phone, install the Trenit app on it. It will tell you real-time platform info, arrival info, etc. so you'll know even before you get off in Levanto which platform your next train arrives on, whether it is late, etc.