mini BMXs. those that are raced by young kids have 451 wheels
sometimes in sprint rim form
of course the frame will be smaller too.
the PK ripper BMX had and adjustable brake mount. So could use either size of wheel.
I built a BMX with 3 speed 406 alloys from a shopper bike.
I made the seat pin out of a long tube of metal from a garden frame. I put another tube inside it. That bike had 180mm cranks. Im 5 foot 8" I have since got a long BMX seat pin. Heres it on my Puch Mini sprint. Its 22.2mm diameter tube
A lot of BMXs are using thicker seat tubes these days. 25.4mm is common. Which is also a common size on normal bikes. Ive got a long Kalloy seat pin in my Gold bike. A 1970s Raleigh Phaser. Thats a 25.4mm post, and quite long.
I did manage to build a BMX. An 1980s Raleigh Wildcat with a 451 5 speed deraileur gears. With out widening the rear stays. Just messed with the axle spacers and the spoke dishing. I dont have a picture of that bike in 5 speed form. But here it is with mags on. Those old Raleigh BMXs had the R20s thick seat tube. So I cut out a seat tube from an old road bike and inserted it into the frame to extend it to my size.
you might have to run the saddle in the furthest forward possition. As small bikes have a lazy seat angle. So the seat lays way back when on a long post.