If you get to a more woodshop kind of store, you can buy the thin wood strips, about 3/4" wide by 10' long or so. It comes in 2 styles. The you glue it on and wait to finish it, or the factory installed hot glue on the back kind.
The hot glue kind installs with an clothes iron and can be finished immediately.
Figure about $1 per foot, usual types, oak, maple, mahogany, birch, pine.
Glue it on to cover the edge, then use your laminte trimmer to get rid of excess.