I don't think you can choose what Bitcoin you have in your electrum wallet that you can spend but I know you can choose what address you will send it from, and if Mr. X knows the tx id of the transaction then expect that he also know where the BTC is going.
Actually, yes you can choose exactly which Bitcoin (UTXOs) to spend from your wallet.
Using the "Coins" Tab (Might need to use "View -> Show Coins" if you haven't enabled the tab already). This will show you ALL the individual UTXOs controlled by your wallet:
You can think pick and choose exactly which ones you want to spend (ctrl+click, shift+click etc):
And then you can "right click" and "spend":
And your "send" transaction will be created from JUST those UTXOs:
NOTE: Electrum just uses these UTXOs as the "available" UTXOs for this transaction, it won't necessarily use ALL of them. That is to say, if the amount you want to send does not require the use of all the UTXOs to, then Electrum will only actually use the ones required to cover the amount+fee.
So, if you absolutely wanted to include ALL the UTXOs (for consolidation or obfuscation or whatever), you would need to manually specify your "change" address as well by using Electrums "pay to many" functionality and some tricky maths to work out the amounts to send to each address etc