Having kept an eye on the Kaupthing Singer and Friedlander IOM debacle, I'm not convinced the offshore guarantees are worth the paper they're written on.
These are very small countries. The original IOM guarantee was 75% of up to £20,000. But this was based on a post-collapse levy on other financial institutions, which was capped at something like £5m/year. With only 30 banks active, that means there's only £150m/year available. Kaupthing had billions under deposit.
Secondly, the Tynwald (IOM parliament) spent a long time faffing around trying to put an improved protection scheme in place before they declare Kaupthing in default. That meant people had to wait even longer to get any cash out at all (many had put their entire savings in there and were living off the interest, which stopped). I get the impression that collapse completely overwhelmed the small island government.
Kaupthing originally had a guarantee that funds in KSF were 100% backed by the parent company. But the UK government did some fancy footwork so they got first dibs on the assets, which left IOM savers further back in the queue. I'm not up to date on the current position, but as far as I know there is still a substantial proportion still to pay back if there remains any cash left to pay.
Guernsey didn't have a guarantee at the time, so Heritable (Landsbanki Guernsey) went under without that protection. I'm not familiar with what happened (KSF IOM had a lot more savers, so made a bigger media splash).
All three (with Jersey) have beefed up their protection, but fundamentally how much cash does a small island have if the institution goes under? The UK won't bail them out.
I don't have any experience of 'proof of funds', but sometimes they want two sorts of proof: one being a bank statement showing where the funds are now, and another showing how you generated it. I imagine a pile of P60s (that's end of year earnings, same as in UK, right?) would suffice for savings from employment income. If you inherited, or sold a house, or whatever, then proof of that (even if it was a long time ago) should be sufficient. I don't think they're that bothered with the interest you've earned in the meantime.