When your wallet pops up a “Please sign” window, what exactly are you signing?
First, what it is: Every transaction from an Ethereum externally owned account has an incrementing nonce. The same nonce can only be included once, which prevents the same transaction from being executed repeatedly.
Why it matters: A signature request from your wallet may not be a transfer. It could also be a token approval or an off-chain signature, and signing it could have an effect similar to making a direct transfer.
When you transfer out $BTC , your wallet signs the transaction with your private key, and nodes across the network verify the signature using the public key.
Every potential gain comes with a corresponding risk. Think carefully about how much you could lose in the worst case.