Thanks DuckieTigger and HarryT for your responses.
I know that pressing the power button for 7 secs doesn't completely turn it off. I should I have phrased my question better. Sorry...
What I meant was that perhaps the kindle uses less power in sleep mode than in screensaver mode (I have the version WITHOUT special offers).
I decided to try a cover with a magnet anyway and If I can't adjust I will either try to remove the magnet or find another w/o one.
I bought one from this ebay store
based on the feedback I saw on this thread. I got the black one.
It looks sturdy and is very light. It is fairly easy to put on and to remove. You just have to press one of the corners and then pull from the middle.
It also came with a screen protector which I am currently not using because it makes the screen a bit darker. I guess you can negate the effect by increasing the light intensity.
Overall I am happy with the purchase: 25$ for a cover very similar to the official one.
All that's left is (try to) adjust to using screensaver instead of sleep mode
Once again, thanks to everyone for your help!