Unst: Kept useable - albeit unlicenced - for air ambulance flights. No fuel or navaids. Owned by the Shetland Islands Council (SIC). Contact them for permission. Occasionally used for other purposes eg the car club's annual drag races.
Scatsta: Tower, NDB & SRA approaches available. No avgas. May need permission but I can't remember. Was never a factor for us when I worked for Loganair up there.
Tingwall: Licenced. Fuel may be available for sale. Depends on the fuel stock & Loganair's needs (it's their own fuel). No instrument approach but does have an NDB. Watch out for the rising ground all around the strip (it's in a valley) and be careful about the wind turbines to the S - especially if you're departing into IMC & the wind is westerly.
Don't forget Sumburgh: Licenced. Tower & various instrument approaches including ILS. Avgas available.
Half a dozen other airstrips in the Shetlands. Some are easy to fly into, others rather challenging eg short (381m with obstacles) or even impossible if the wind is above ~15-20 kts from the wrong direction(s).