I saw your mention of this Ni80 NiChrome wire on another forum ( Kampfgruppe144 I think ) and had a look around to see if I could find a source. Lots of sources for NiChrome wire but nothing this small. 0.05mm is about 42 or 43 AWG. I have a spool of 38AWG ( 0.1mm ) copper wire which I use for some things.
Seems the vape shops don't have anything this small over here.
But I did find a suitable alternative.
Molybdenum cutting wire. Commonly used for separating the screens of smart phones during repairs. Also called LCD separator wire, screen cutting wire, or various other combinations of LCD, screen, smart phone, separator, separating and cutting. eBay, Amazon, and your other friendly online Asian sources list many.
Available in many sizes from about 0.03mm ( 0.0012 inches - smallest I can find ) to 0.1mm or so. 0.04mm, 0.05mm, 0.06mm sizes seem to be pretty common.
Molybdenum is pretty tough but I can cut the 0.04mm stuff I found with a sharp scalpel blade although I do tend to use a pair of cutting tweezers similar to these:
https://www.ideal-tek.com/scheda.php?m=search&f=8&c=Cutting%20Tweezers&l=3&idp=58 simple and intuitive to use, they get a lot of use and I don't know I managed without.
I can't wait to see how you get on with the rigging. This small wire is just about at the limit of my vision and my BFF ( Big Fat Fingers ).
cheers, Graham