Grafton banjos in UK makes a fretless banjo. It does look different from the traditional ones, looks more like a modern banjo without the frets. I have a Grafton fretted 5-string banjo and I am happy with it. Look at https://www.andybanjo.com/ current cost of their fretless banjo is >£400

Have you thought of getting an instrument maker to make you one? That will be expensive I suppose.