I inject twice a week too. What I've been doing for the last 22 months on TRT, is filling 2 syringes at a time. I open the new vial, swab the rubber top with an alcohol wipe, and fill 2 syringes. Then I tape the top of the vial back down until the next week. But if you're splitting the small vile into 2 equal doses, just fill the 2 syringes, and it should be empty. That's the easiest way I've found.
In the first month of TRT, before I realized I didn't have to get my testosterone in pre filled syringes at my dr.'s pharmacy, I had 1 syringe with the entire week's dose. Seeing that I split the dose into 2 injections a week, I injected half on Tuesday evening, then put a new needle on the syringe for Saturday morning's injection, with the remainder in the syringe.
Now, I had no problems doing it that way temporarily, I wouldn't recommend it long term. Syringes and needles are really cheap, so why take a chance with infection of you don't need to.