If you're based in the NE of England it is fairly 'doable'. Yes the weather at either end of this trip can be pretty horrible - but the difficulties really only kick in if you are committed to the whole thing on a particular day(s).
With a period of settled weather it is just a long trip within not that many alternatives (or fuel sources).
But the great thing (and most infuriating come to think of it) about Scotland is that the weather systems are generally different from east tot west and often from north to south of east and west. So half of the trip is likely to be possible most of the time! Obviously you can also chose which way around you do it following the weather or pushing through it.
Whilst Barra is a fairly interesting destination, Unst can epitomise bleak. So it is not much of a destination. 'Doing' Orkney and Shetland as a standalone trip can be really good. The outlying strips in shetland are pretty rugged so the right aircraft makes things a lot easier. Orkney in comparison is much more civilised and there is a great deal more to see tourist-wise.
So much however depends on whether we have another MetOffice 'barbeque summer'.