And if so, is a Fairy Ninja the best choice?

I don't think a W6 solo is possible because of the inventory space needed for the undroppable quest items. W7 is soloable easily, combat is even easier than with a party because of the higher character level. For most power and access to all spells switch through the classes and end up as Fairy Ninja.

I was thinking more about this.

What if I take a full party in Wiz 6 and get 5 of them killed? Can I then use their inventory space to carry whatever I need while only playing with one active party member? Would this work in Wiz 7 and 8 as well?

Afaik W6 simply doesn't allow starting with a single character. Hence I stopped playing before I began and can't possibly call myself knowledgeable regarding W6. W7 & W8 can certainly be solo'd.

Regarding the Faery Ninja: W7 has You change classes a lot. Actually I stopped my run somewhere half way through, but had already assembled all spells of multiple schools as a Fairy and reverted back to ninja. Guess it's a decent choice at least. Due to that (franklly ridiculous) class changing mechanic You could just play "everything and then some", ending up with any class You'd find fitting for W8. Without class changes it becomes infinitely harder. Possibly impossible, at least for anybody that didn't play through W7 multiple times and has it all mapped out beforehand. Even with class changes it remains a challenge for a W7 beginner that stumbles half-blind through it. Generally I had the impression it's easier to solo than W8 and at least possible with very little experience regarding W7. Honestly though? I found it a bit too frustrating at times, because I was such a noob and had bloody tough fights w/o reward, because I had no clue where to go and what's actually worth fighting for, or in which order. I hate to admit it, but it's probably more fun to play through these games the normal way first and return for the solo once You know what You are doing. A party w/o class changes might be almost as challenging as a class changing solo and likely makes for a way more rounded experience.

As far as W8 goes the faery ninja is a good choice, though not necessarily the best. Early game is hardest for the most part and that's not when a faery ninja shines. He definitely does later however, so I guess he's a top tier solo char anyway. He becomes a good char once he got his stealth up, more so when getting the cane ofc (which is a likely yet random drop). In a non-IM expert solo all classes work, though Mage & Psionic are definitely a tier of their own - the worst tier by far ;)