Blake and
Blair don't sound unisex to me, and I don't like either (but
Blake is a little better than
Blair.
Blair is like bland, blare, blain, etc).
I'd be willing to use
Briar. I think it is unisex but I prefer it for a boy.
Some others:
Brenn
Bryn BreeBranBailey BronteBennett (maybe)
Bevan (maybe)