hmmm ... that's not so easy in this case. If you don't have your own RIPE block which you can route yourself, your IPs are actually belonging to your provider and you are only renting them. It's very unlikely that your provider will allow you to route his IPs to a another provider.
I guess your only chance to switch your services from one server to another with this setup is to change your DNS to route to the other IP in case of failure. That's not really a great solution, because this means your services will be down until the dns propagation time is over, but the only solution I see in the moment.