The runway at Baltasound is still in good nick, but is no longer in operation and at 2,000ft, there are plenty of FW ac that could get in, but not many that could get out again!
The standard method, as mentioned earlier, is to fly into Sumburgh with Logan Air (FlyBe stopped flying there about 9 months ago) and collect a hire car; when the 2 ferries are running, allow about 3 hours.
That sounds pretty horrid journey, but the roads are now excellent and lack of other traffic (if you avoid Lerick) make the journey an absolute joy. An hour each way can be lopped of the journey time by landing at the privately-owned Scatsta - 3,750ft (if you have your own aircraft and ask very nicely). They used to take BAe-146s,
The only Eastern Airways flights are private charters for Sullom Voe Oil Terminal or off shore - most of the rotary activity that used to operate out of Unst seems to go from Scatsta now.