From my notes, I see there are two types of sea buckthorn oil -- oil from the seed only and oil from the seed and berry. The fatty acid profiles of the two types look to be quite different, so do you know which one the other soap makers are using?
I use rosehip oil in lotions and body oils. It also comes in these two types, and the seed oil is supposed to be the nicest for skin. It can be hard to know which type a supplier is selling, however, because they don't always specify the type. I suspect that's because at least some suppliers don't know there's a difference.
The seed oil is very high in linoleic and linolenic acids, which will make the soap more prone to rancidity. I'd look into using ROE (rosemary oleoresin) and a chelator to minimize rancidity or plan to make small batches and use the soap reasonably quickly. Alternatives would be grapeseed and hemp seed.
The seed and berry version is roughly similar to rice bran oil. I'd think this one will be more stable if used to make soap, but it's not as rich in the polyunsaturated fatty acids so less desirable if you want to make soap high in these FAs.
Remember that NaOH will break any fat apart into fatty acids and turn those FAs into soap. The properties of any fat used to make soap do not survive in the finished soap -- it's the properties of the fatty acids that transfer over into the properties of the soap.
If it's the color you're after, there are other less expensive options that might be acceptable. Two possibilities -- an oil infusion of annatto seeds or unbleached palm oil.
There's nothing wrong with using sea buckthorn to make soap if you don't mind the expense. I don't think the soap is going to be any more amazing than less expensive fats, however.