If you use screw on brake adapters the right-hand wheel will be fine (disc on it's left) but the left hand one (disc on it's right) will want to undo as you apply the brakes. I have used this method and glued the adapter plus bolted the disc through the hub. It's a bodge rather than a proper job but it worked fine even under extreme braking. See top picture. You really want hubs that are designed to take a disc direct not the disc screw on adapter. You'll be exceedingly lucky to find any ready made wheels that will do the job. Regular 3/8 axles will not take the strain. 12mm, 14mm, 15mm and 20mm will all be ok. Of them only the 14mm regularly comes in a 20" wheel and almost (rocking horse droppings levels of rare) never with disc brakes so it's a case of lacing a pair of suitable hubs into some 20" wheels. It looks quite daunting doing your own lacing but frankly it's simple though time consuming.
I laced a pair of each of these myself. Both 20" nominally! One with a 20mm axle and one with a 12mm.