Cyprus non-dom requires that you have a company in Cyprus, receive an income from the company and rent a flat. So I think what you said about Gibraltar company and Cyprus residency would not work.In Cyprus, you're looking at zero tax if your income is coming from abroad and is in the form of dividends. There's a similar scheme in Malta, where you pay no or very little tax on a remittance basis. The main caveat is the company paying the dividends must truly be an overseas company, which would mean you might want to – for your own peace of mind – take steps to ensure the company is tax resident in Gibraltar. Pretty easy to satisfy by appointing directors resident in Gibraltar.
Otherwise, if you live on purely dividends or other capital gains, you might want to look into Switzerland, Luxembourg, Belgium, and Slovenia. There are different rules for different circumstances so depending on your situation, one of those might work out. Monaco (assuming you're not a French citizen) and Andorra could also work.