I think you guys didn't catch that OP is looking for a knife that uses single edge RAZOR blades, not utility knife blades.
Yeah, if I understood the OP, he's not looking for a folding utility knife.
I've got both styles in the attached ebay pic (correct me if this isn't what you're looking for). The smaller all chromed steel slider is fine for kitchen drawer duty cutting packing tape, zip ties, and whatnot. The larger wood- handle version seems like it would be great cutting cloth or paper with a straightedge on a mat, but I don't use mine- it's squirreled away in a box somewhere at the moment. I've still got a ton of blades left.
ETA, I don't use it because almost always I've got a utility knife (non- folding for me thanks) with a fresh blade handy, which works fine for me.
FWIW, when I was painting years ago I used a basic sliding scraper for utility knife stuff, and it worked fine, with the advantage of having the entire edge exposed. If a corner was roached from cuttting against a hard surface, the middle could still cut thin plastic sheet, tape, etc.