Oh dearest Julia!
I can't give you a detailed proc. - in fact, i never heard anyone use this route to purify nitroalkane. But it definitely must work. All nitroalkanes are acidic in nature and react w/alkalis, forming water-soluble salts (explosive when dry!). I ain't sure 'bout the alc. NaOH test - but i frequently seen mentions of it in the old Russian books - unfortunately, they never said
what is actually the result of the test, but it's been my impression that a precipitate.
The whole idea is to slowly w/stirring and cooling drop nitro into aq. alkali (the experimental part for that can bee found in the link below), clean out the impurities (like by xtraction or separation or whatever) and then carefully acidify it, also w/good stirring, salt out, separate. The competing rxn is Nef rxn of the nitro to (acet)aldehyde - it is the prevalent one when adding salt to acid. See
https://www.thevespiary.org/rhodium/Rhodium/chemistry/nef.html
for the details.
Anyway, testing this on a small qtty of your product won't hurt
Antoncho
P.S. Rhodium, if you're reading this - the link at your page says 'nitroalkenes', not 'nitroalkanes' as it should bee