It is possible that the BSW thread will mate with that diameter UNC but you wont be able to screw them together by hand.....the resistance will be pronounced, even at that small diameter.
If you have a vice or molegrips or whatever then you are in with a chance.
Id try to fit the UNC rod into the knob first and then leave it be - the dome nut should be easy enough once the cut length is done.
John
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