Planing laminate is not the way to go for two reasons:
1) planing laminate almost always leads to tearing the face of the laminate.
2) The substrate under laminate is very often chipboard. You don't plane chipboard.
I would use a router with a guide, which would leave you nothing more than two rounded corners at the ends, which you can solve with a fine tooth saw and a file.
If you attempt a jigsaw, you need to tape the face of the cabinet to reduce blowout, as even the finish blades hurt some laminates. I wouldn't use a jigsaw for the simple fact that it's very hard to cut a perfectly straight line.
As others mentioned, if you can see the new edge, you'll need to pretty it up a bit. It doesn't necessarily need to be an exact match as it's hidden by the fridge, but you'll sleep better knowing that it's pretty again
thanks,
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