Your script says “hero cuts the rope with a small knife”. So, you need a small knife. Well, one thing you can do is to craft one from a piece of aluminum bar.
Mark your pattern out on a piece of aluminum flat stock. This is 1/8″ thick and about 1″ wide. Something like this probably costs $10 at the local hardware store.
Cut it out with your hand tools.
Hammer the blade to add some texture and to thin the edge.
When you hammer it, the metal will bend away from the hammer marks.
Use some sandpaper to ensure the blade edge is dull so no one is hurt.
Cut two pieces of thin wood for the handle.
This is the type of epoxy I use. It is two part, and can be found at the local hardware store.
While the handle is still rough wood, spray the blade black.
Shape the handle.
The rough knife is basically done.
Sand the handle.
Stain the handle.
The handle is stained, and the blade sanded a little to allow some of the silver looking aluminum to show through.
Distress it again with some sawdust.
There is your finished blade, ready for the hero to cut the rope.
So, a knife like this would cost you a few dollars in metal and wood and glue. It takes a day or so of labor. The aluminum is really light weight. This can be good and bad. Your actor may have do some acting to make it seem like a real heavy knife. This technique can be used to make a sword as well. It takes smaller tools than real steel. Aluminum is easier to form and shape for people with fewer tools.
Go ahead, make a mess, make a knife, have some fun.