Andy
Whether or not it is Prince Andrew in the SK pictures, we can safely say the SK pictures and the picture of Prince Andrew and his bearded companion in Stanley are not linked. In the SK pictures, the pilot is wearing camouflage clothing. Prince Andrew in Stanley is wearing a camouflage jacket but it is on top of a goon suit (survival suit).
I'm also doubtful that the Stanley companion is the pilot in the LHS of the Seaking. Yes he is bearded but lots were at that time. ASW Seakings had a crew of 4, so every possibility that he was an Observer or an Aircrewman. I think he's the Observer and I have a name in mind but let's see what any ex 820 crews have to say on the matter.
So back to your initial question - is it Prince Andrew in the Seaking? You'd better send a polite enquiry to Buckingham Palace!