We have a simple lamination machine at home, I use it quite a bit and it's quite effective.
The two sheets of laminate film are simply bonded together with a heat sensitive melt glue, the rollers heat up and melt it as the sheet is pulled through.
If you space the labels apart on an A4 sheet (I suggest 8 or 10 mm spaces) the two sheets of laminate should bond together between them so you can cut between the labels and still retain a waterproof border. My advice is to use the hottest / slowest setting on the machine but you will probably need to experiment.