Interesting. Thank you for sharing your thoughts. I was wondering about sunflower oil as a substitute because I can get it locally at a great price and it has no smell whatsoever, that I can discern anyway.
Be careful about this Valerie. I believe she was thinking of the high-oleic sunflower oil, which is a special type that was developed through plant breeding.
HO sunflower is a very good oleic soaping oil in the same ballpark as olive oil. I get it from SC and use it quite a lot. It's light colored, essentially odorless and low in linoleic acid.
Unfortunately it's pretty likely that your local suppliers of sunflower oil have the ordinary linoleic variety. I would not consider that suitable for soaping, and most others would probably say it's only suitable in small quantities.
The important point is that these are two entirely different oils even though both are produced by sunflowers. They will produce entirely different results, so there needs to be explicit labeling to tell you what you're buying.