Terry, I'm no sight guru but have repaired several Lymans of various vintages and can offer some info, but only as it applies to Lymans. Yours may require a different approach.
First, you may have left-hand threads on your shaft, not a huge problem but will require either tooling or imagination.
Second, cut threads as opposed to rolled threads are almost always either too loose or too tight (and soon get too loose) if not done by an expert with, again, the proper tooling. Unfortunately I am no expert machinist and especially not on such small items.
Third, for a quick-&-dirty fix that used to be seen with Lyman 48s used on older 1903s and similar, simply file a tiny screwdriver slot in the broken end of your shaft. Seems that many owners of iron-sighted 1903s had a problem with the windage knob being inadvertently rotated by slidng into or out of the gun case or saddle scabbard, and so to prevent this they simply removed the knob, shortened the shaft (or not) and filed a slot for adjustment. Probably many of these short shafts were originally caused by accidental breakage, as yours was, but I've seen this alteration on many an older 1903 and I'm sure some were done deliberately.
Fourth, it might be worthwhile to investigate repairing your original shaft. A good workman could possibly silver-solder or braze or even epoxy an extension onto the shaft's broken end to accept your knob.
Food for thought, good luck, Joe
