I’ve made several nuts from bone blanks and I’ve even made one from a small piece of hard wood. It isn’t hard to do but it’s not easy and it takes (me) a long time. None of my Ukes are that good, all bar one are laminate, so my experiences might differ from other people with much better instruments. Does nut material matter? Well it has for me so I try to avoid even the better hard plastic nuts, but YMMV.
33mm wide at the over the tuner end of the fret board seems like an unusually narrow neck to me. As others have said buy a pre-made nut and (equally) file a little off each end to bring it down to the size that you want. Some nuts have wider spaced string slots than others, the OP might like to check out how that impacts on his instrument. Perhaps that’s too much detail, the important thing is to make a start; fit what you can and then see what might need to be done from there. Of course, OP, once the nut is fitted, don’t forget that the Uke will need to be ‘set-up’ too.
Edit. I used hand tools only, worked slowly and encountered no particular hazard issues - perhaps I was either lucky or managed them automatically. Stuff happens and whatever you do always consider H&S issues, and especially so when using power tools.