Hi Neven,
Can I buy you an SSL certificate, so you don't have this warning all the time? GoDaddy has them on sale at £3.99 per year. I could buy a 5 year one and worry about it expiring later.
I'd probably need to authenticate the domain, so you'd need to be able to change something on the root of the site or DNS entry. Would that be OK?
Cheers, Seumas