ONE-STRING FIDDLE - DEVELOPMENT

Use half matchsticks to make FRETS. When the glue is completely set you can break off the extra that sticks out and sand the ends smooth
If you look at a guitar you will see a number of metal ridges across the fingerboard. 

These are called FRETS and you will notice that the spaces between them are not equal. You can transfer these positions to your fiddle even if the two instruments are different lengths.
Cut a length of wood or thick card the same length as the free part of the guitar strings. That is from the slotted ridge [called the NUT] at one end to the bridge at the other.
Mark the positions of the frets - you won't need all of them, then fasten a thread to each mark on your 'stick' and attach a small weight - felt pen? - to each thread. When you tilt the stick the threads will move closer together and you will be able to adjust the angle until the end threads match the distance on your instrument. SEE DIAGRAM
There are many possibilities. Why not use a card or wooden box?
You will have to redesign the instrument maybe - but it shouldn't be any more difficult. The two pictures here show two different models that use exactly the same pieces.

Here are a few problems for you to think about

How can you stop the string slipping off the bridge?

Can you design a method for tightening the strings?

(When the string is tightened it plays a higher note)

Why do stringed instruments have holes in the sound boxes?