Well we are doing BLW but if something is like a puree anyway, we give that to Leyla too. She had mashed potato and ate it with her hands the other day... it went everywhere!!! She really enjoyed it though. I also have some 'baby muesli', which I thought would just be muesli with no sugar or salt but it turned out to be mostly pureed with a few bits of oats in it. Rather than throw it away, I've been giving her that on a spoon. I normally hold the spoon for her at the start - I just hold it in front of her and she lunges for it if she wants it, then towards the end I put a bit on the spoon for her and she takes the spoon herself. If she wants to dip her hands in it, I let her too.
With traditional weaning, I think the purees are quite runny to start with, I might be wrong though. I wouldn't try letting LO eat those with their hands, they just wouldn't be able to get much! You could try thicker purees that would stick to their fingers though, or giving something like bread or vegetable sticks to dip into the puree. Leyla actually seems to prefer to eat them off a spoon though, whether I'm holding it or she is. I suppose at some point she will be exposed to adults eating with hands as it's what OH's family do, but we don't tend to have that type of food at home so she hasn't seen it much yet. I guess when she does see it, she'll learn to eat that too but it will probably mostly be solids.
Sorry if that was rambly and not much help!