I’ve finally found a way to execute occ (see my howto to do this on an 1&1 aka Ionos service) and given this, I could convert the database in the “standard” way 
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But if your shared service doesn’t include any MySQL or similar database service out of the box (can you check again? Many shared services include a number of MySQL databases in another section than webspace?!??), I suppose it’ll get very hard to run such a database on that server!