It was a little hard finding a self contained message signing page. It shouldn't be.
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If you don't want to install a full wallet, you can take this route.
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Just installing bitcoind and running bitcoin-cli signmessagewithprivkey offline worked like a charm.
No need to download the blockchain whatsoever so this is a very fast (2 minutes install time) and secure way to generate signed messages.
Thx to all for the explanations.