Finally done!

I contacted blockchain.info and they told me 2 things

1 - There is no way to sign messages with the new design.
The only way I was able to do it is to export the private key, and then import it to the key to a new blockchain.info account, without switching to the new design.

2 - Concerning exporting the private keys to another wallet.
That's what they answered.
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There is no user-friendly way to export individual private keys from the HD wallet, but this guide will walk you through the steps:

https://docs.google.com/document/d/1-2l6xOqcbjs9QWEqSh72RD1d8EEdvG_hQuEXw_f_o6w/edit

Thanks,
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Already contacted Theymos with my signature, waiting for his answer.