The reason why I am dubious is because my mum bought a beautiful, huge victorian pine bookcase, shelves with glass doors on top, cupboards below, and proceeded to cover every bit in Fablon, that popular green linen/tiny check version, as she wanted to station it in the kitchen. It never looked smart and over the years became even less so. Eventually she had her kitchen refitted and gave me the piece. We got every scrap of fablon off, restored the wood and now it looks very handsome as a bookcase on the landing. So I am prejudiced, sorry.
Would you feel happy about painting them. You can get paint which covers melamine or acrylic type paint might do a good job. I used eggshell on wardrobe cupboards and that was very successful. I recall my efforts with fablon etc years ago. It's not a happy memory. You can always try paint out on inside cupboard door.