This is a trip that we on Sumburgh Radar see fairly often - although usually it is ferry flights passing over us in the other direction en route to landfall in Norway somewhere.
The most recent one I worked was a Norwegian AS32 helicopter transiting at 2,000ft from Norway to Vagar.
Air Traffic wise we would provide you with a "flight watch" as long as we could which would be dependant, obviously, on your level. At FL65 (correct quadrantal outbound) we would be able to maintain a listening watch with you all the way to Sider by which time you should be well within range of Vagar AFIS or Reykjavik Centre.
If you flew low level (say around 2,000ft) we would suggest you transferred your "flight watch" to one of the oil rigs that are out to the west of Shetland on the Atlantic Rim. It would then be a matter of "hopping" from frequency to frequency just so you had an Alerting Service from someone who could shout for help should the unthinkable happen.
Any ATC questions regarding this trip, or for any flying around the Shetlands, then feel free to ask.
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Odi