What I would do with Electrum is that I would send the funds to the recipient and specify the mixer address as well with a random amount as a placeholder, go to the transaction preview, see how much of the amount I'm left with after the fees and adjust accordingly such that the change is not sent back to anywhere else.
There is a simpler solution in Electrum using the pay-to-many function. Just treat the change as a "send all" as you would to any other address.
In the address box on the send tab, enter the address you want to pay, followed by a comma and a space, and then thr amount you want to pay. On the next line, enter your replacement change address, a comma, a space, and an exclamation point. The exclamation point tells Electrurm to send all remaining funds from the transaction to that address, and will automatically update the amount as you adjust the fee. Your transaction will look like this:
bc1paymentaddress, 0.123
1notreallymychange, !