I've read stories about people replacing the volume control/power switch that was supplied with the BITX40 simply because of the 4 mm shaft! There are ways to adapt it to your favorite knobs.
I was in a rush to get my first BITX cased and operational so I filed that nylon shaft down to size for a knob that I had. It works, but took more effort than it should have.
A friend of mine is adept at salvaging parts from the recycling bin. I had never considered using toothpaste caps and container lids for knobs but his builds look much better than mine! Some of those lids are just perfect; fluted, colorful, and large. A bit of glue, maybe an old damaged knob for a base and you can have a one-of-a-kind creation.
My second BITX was simpler. I'm learning. I used a couple of layers of heat shrink tubing to build the shaft out to fit ¼ inch knobs.
Most of us use heatshrink tubing to insulate splices, connector pins, and component leads in tight places. I like to layer progressive lengths and diameters to use as strain reliefs on antennas and microphone cables. It is flexible stuff, to a degree, and makes for good weather proof coverings for splices. However, it can be stiff enough to form a good hard surface to support a knob on a shaft.
Cut the shaft of the control to the desired length. The small 4 mm nylon can even be cut with flush-cut wire cutters. Then cut a length of heatshrink to match. Use the dense tubing material and the size to just slide over the shaft nice and snug. Gently heat the tubing so not to distort the nylon shaft. Let it cool before slipping on the next layer. When it cools you will note that the flat side of the shaft is still evident on the new, expanded, surface. Your ¼ inch knob now slips on with a good fit and the setscrew seats firmly and with no wiggle or wobble.