I thought hair sheep, like the Barbados black belly, had short, straight coarse hairs, sharp at both ends, and that they were scattered as shed.
For spinning you need wool, which has scales on the shaft of each fibre, so they cling together in the yarn.
If it's not having to shear which makes you interested in the hair sheep, go for a shedding breed such as Soay or Shetland. They
can be shorn, but can also be roo'd, where the fleece is separated from the new growth in small tufts, by hand, no shears involved. In fact this is a great way to collect fleece for spinning, as sometimes you can spin direct from the tufts, or card each tuft into one rolag, and you get no noils from double cuts.
Roo'ing can take some time, but is one of those jobs when you can commune with your sheep in the sunshine.
Try spinning a variety of different breed fleeces before you decide to keep a particular one, so you know what suits you.