I spray veneer softener on both sides of paperbacked veneer all the time, especially on pieces I’m going to be bending over an edge with a roundover. Don’t soak it. Just spray enough so it’s covered. Also, I don’t put as much on paperbacked veneer as I do raw wood veneer.
If the sides of the cabinet are flat (no roundovers) and your veneer is pretty flat you may not need the veneer softener.
Then again, i don’t use contact cement. I use Heat Lock glue and an iron. You put glue on both the cabinet and veneer and let it dry, similar to contact cement. The difference is once the Heat Lock glue dries, it won’t stick to itself until heat is applied. That allows you to reposition the piece when you put it on and prevents a mess if part of the veneer touches the cabinet before you are ready for it to.