You should be able to take the actual tape from the cassette and put it into another cassette. I've certainly done this with audio cassettes.
Both cassettes need to be ones which are screwed together. Otherwise you will not be able to do this.
There isn't a procedure. My tip would be do it carefully. The main problem you will have is that these things tend to spring apart when you undo them. So lay them on a table and carefully unscrew both and remove the faces. Note how the cassettes are laced inside and where all the parts go. Take time to study and record how they go back together. This will save you time in the end.
Lift out the spools and put them into the new cassette making sure that all the bits are replaced exactly as they were. Make sure that you put the spools back with a similar amount of tension and not loads of slack.
If you want to test the cassette before putting it into your VCR, puch in the little button which you'll find at one end. This will allow you to lift the front flap which protects the tape in the cassette. It also releases the spools. Rotate these to check you assembled the cassette properly.
Anthony
November 2003