I've removed the plastic laminate off of 20 square edge counter tops so far, and I just pry it off. I HAVE HAD some of the substrate plywood come up with the laminate, tho, but I expect this is much less likely to happen if you're removing the laminate from a hardwood (which is much stronger than fir plywood).
Toluene dissolves old solvent based contact cement, and would most likely dissolve any old finish on your cabinet as well.
If you can't find toluene for sale anywhere, use lacquer thinner, which is typically 70 to 80 percent toluene. Both toluene and laquer thinner are very flammable and volatile, so provide plenty of ventilation when working with them. Also, both will evaporate completely without leaving any residue.