Re: What is the minimum transaction fee in the different wallets ?
I believe that you can send any value of transaction provided the fee is appropriate for the size of the TX. I assume Bitcoin core would allow you to do something like this. You can also generate TXs manually and broadcast it to blockchain.
No... he isn't concerned about the value of the transaction... he is concerned with minimum fee and sending TX where the fee isn't appropriate to the size 
OP can just use latest version of Electrum (2.8.2), and select "Edit Fees Manually" from "Tools -> Preferences -> Fees"... then when he goes to send the transaction, he can set whatever ridiculously low fee he likes
Just bear in mind that the Electrum servers (and/or Bitcoin Network) may not relay your transaction if the fee is too low.